Questions and Answers
What is the relationship between the gradient of a line and its inclination?
What is the inclination of a vertical line?
What is the gradient of a horizontal line?
If a line has a negative gradient, what can be said about its inclination?
Signup and view all the answers
What is the equation form used when given a gradient and a point?
Signup and view all the answers
What is the condition for two lines to be parallel?
Signup and view all the answers
What is the relationship between the gradients of two perpendicular lines?
Signup and view all the answers
Which form of a line's equation allows us to easily read off the gradient?
Signup and view all the answers
What is the first step in finding the equation of a parallel line?
Signup and view all the answers
What is the formula for the two-point form of a straight line equation?
Signup and view all the answers
What is the first step in finding the equation of a line perpendicular to a given line?
Signup and view all the answers
What is the formula for the gradient-point form of a straight line equation?
Signup and view all the answers
What is the purpose of the point-slope form in finding the equation of a parallel line?
Signup and view all the answers
What is the formula for finding the gradient of a perpendicular line?
Signup and view all the answers
What is the advantage of using the point-slope form?
Signup and view all the answers
What is the formula for the gradient-intercept form of a straight line equation?
Signup and view all the answers
What is the trigonometric relationship between the gradient and inclination of a line?
Signup and view all the answers
What is the significance of the constant c in the gradient-intercept form of a straight line equation?
Signup and view all the answers
What is the purpose of using the point-slope form of a line's equation?
Signup and view all the answers
Why is it important to simplify the equation of a perpendicular line?
Signup and view all the answers
When is the two-point form of a straight line equation used?
Signup and view all the answers
What is the process of finding the equation of a straight line given two points on the line?
Signup and view all the answers
What is the condition for two lines to be parallel?
Signup and view all the answers
What is the relationship between the gradient-point form and the two-point form of a straight line equation?
Signup and view all the answers
What is the relationship between the y-intercepts of two perpendicular lines?
Signup and view all the answers
What is the advantage of using the gradient-intercept form of a straight line equation?
Signup and view all the answers
What is the purpose of the gradient-point form of a straight line equation?
Signup and view all the answers
What can be said about the gradient of a line that passes through two points (2, 3) and (4, 5)?
Signup and view all the answers
What is the value of c in the equation y = mx + c?
Signup and view all the answers
What is the advantage of using the gradient-intercept form of a straight line equation?
Signup and view all the answers
What is the condition for two lines to be perpendicular?
Signup and view all the answers
What is the equation of the line that passes through the point (3, 4) and has a gradient of 2?
Signup and view all the answers
What can be said about the graph of a line with a gradient of 0?
Signup and view all the answers
What is the equation of the line that passes through the points (2, 3) and (4, 5)?
Signup and view all the answers
What is the value of θ for a horizontal line?
Signup and view all the answers
If a line has a gradient of 2, what is the value of tan(θ)?
Signup and view all the answers
What is the equation form used when given a gradient and the y-intercept?
Signup and view all the answers
If a line has a negative gradient, what can be said about its inclination?
Signup and view all the answers
What is the gradient of a line that is parallel to a line with a gradient of 3?
Signup and view all the answers
What is the formula for finding the equation of a line parallel to a given line and passing through a point?
Signup and view all the answers
What is the significance of the constant c in the gradient-intercept form of a straight line equation?
Signup and view all the answers
What is the relationship between the gradient of a line and its inclination?
Signup and view all the answers
What is the inclination of a line with a gradient of 1?
Signup and view all the answers
What is the purpose of simplifying the equation of a parallel line?
Signup and view all the answers
What is the main advantage of using the gradient-intercept form of a line's equation?
Signup and view all the answers
What is the first step in finding the equation of a line perpendicular to a given line?
Signup and view all the answers
What is the relationship between the gradients of two perpendicular lines?
Signup and view all the answers
What is the purpose of the point-slope form of a line's equation?
Signup and view all the answers
Why is it important to ensure the given line's equation is in gradient-intercept form?
Signup and view all the answers
What is the formula for finding the gradient of a perpendicular line?
Signup and view all the answers
What is the condition for two lines to be perpendicular?
Signup and view all the answers
What should be the final step in finding the equation of a perpendicular line?
Signup and view all the answers
What is the value of θ when the gradient of a line is 3/4?
Signup and view all the answers
If a line has a gradient of -2/3, what is the value of θ?
Signup and view all the answers
What is the equation of a line that is parallel to y = 2x + 3 and passes through (1, 4)?
Signup and view all the answers
What is the relationship between the gradients of two parallel lines?
Signup and view all the answers
What is the inclination of a line with a gradient of 1/2?
Signup and view all the answers
What is the primary purpose of using the gradient-point form of a straight line equation?
Signup and view all the answers
What is the relationship between the gradient of a line and the constant c in the gradient-intercept form?
Signup and view all the answers
What is the equation of a line that is parallel to y = 3x - 2 and passes through (2, 5)?
Signup and view all the answers
Given two points (x1, y1) and (x2, y2) on a line, what is the first step in deriving the equation of the line in gradient-intercept form?
Signup and view all the answers
What is the value of θ when the gradient of a line is -1/3?
Signup and view all the answers
What is the equation of a line that is parallel to y = 2x + 1 and passes through (3, 7)?
Signup and view all the answers
What is the advantage of using the gradient-intercept form of a straight line equation over the two-point form?
Signup and view all the answers
What is the relationship between the two-point form and the gradient-point form of a straight line equation?
Signup and view all the answers
What is the relationship between the gradient of a line and its inclination?
Signup and view all the answers
What is the value of θ when the gradient of a line is 2/5?
Signup and view all the answers
Given a line with a gradient of m and a point (x1, y1) on the line, what is the equation of the line in gradient-point form?
Signup and view all the answers
What is the significance of the constant c in the gradient-intercept form of a straight line equation?
Signup and view all the answers
What is the primary application of the two-point form of a straight line equation?
Signup and view all the answers
What is the gradient of a line perpendicular to a line with a gradient of 3/4?
Signup and view all the answers
If a line has a gradient of 2 and passes through the point (3, 4), what is its equation in the gradient-intercept form?
Signup and view all the answers
What is the condition for two lines to be perpendicular?
Signup and view all the answers
If a line passes through the points (2, 3) and (4, 5), what is its gradient?
Signup and view all the answers
What is the equation of a line perpendicular to a line with equation y = 2x + 1 and passing through the point (3, 4)?
Signup and view all the answers
What is the gradient of a line parallel to a line with a gradient of 2/3?
Signup and view all the answers
If a line has a gradient of -1 and passes through the point (2, 3), what is its equation in the gradient-intercept form?
Signup and view all the answers
What is the equation of a line perpendicular to a line with equation y = x + 2 and passing through the point (1, 3)?
Signup and view all the answers
If a line passes through the points (2,3) and (4,5), what is the value of m in the equation y=mx+c?
Signup and view all the answers
What is the equation of a line that passes through the point (3,4) and is parallel to the line y=2x+1?
Signup and view all the answers
If a line has an inclination of 30°, what is the value of m in the equation y=mx+c?
Signup and view all the answers
What is the equation of a line that is perpendicular to the line y=3x-2 and passes through the point (1,1)?
Signup and view all the answers
What is the value of c in the equation y=2x+c if the line passes through the point (2,5)?
Signup and view all the answers
If a line has a gradient of -1, what can be said about its inclination?
Signup and view all the answers
What is the equation of a line that passes through the points (3,2) and (5,4)?
Signup and view all the answers
If a line has a gradient of 3, what is the gradient of a line perpendicular to it?
Signup and view all the answers
What is the equation of a line that is perpendicular to the line y = 2x + 3 and passes through the point (1, 4)?
Signup and view all the answers
What is the purpose of the gradient-intercept form of a straight line equation?
Signup and view all the answers
If two lines have gradients of 2 and -1/2, are they perpendicular?
Signup and view all the answers
What is the gradient of a line that is parallel to the line y = 3x - 2?
Signup and view all the answers
What is the equation of a line that is perpendicular to the line y = x - 2 and passes through the point (2, 3)?
Signup and view all the answers
If two lines have gradients of -2 and 1/2, are they perpendicular?
Signup and view all the answers
What is the equation of a line that is parallel to the line y = -x + 3 and passes through the point (1, 2)?
Signup and view all the answers
If a line has a gradient of 1/2, what is the gradient of a line that is perpendicular to it?
Signup and view all the answers
If a line has a gradient of -2, what is the value of θ?
Signup and view all the answers
A line passes through the points (2, 3) and (4, 5). What is the value of the gradient?
Signup and view all the answers
What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (1, 4)?
Signup and view all the answers
If two lines have gradients of 3 and -3, what can be said about the lines?
Signup and view all the answers
What is the value of tan(θ) for a line with a gradient of 1/2?
Signup and view all the answers
What is the equation form used when given a gradient and a point on the line?
Signup and view all the answers
If a line has a gradient of 4, what is the value of θ?
Signup and view all the answers
What is the equation of a line that is perpendicular to the line y = 3x - 2 and passes through the point (2, 1)?
Signup and view all the answers
What is the condition for two lines to be parallel?
Signup and view all the answers
A line has a gradient of -3/2 and passes through the point (2, 3). What is the equation of the line?
Signup and view all the answers
What is the main purpose of ensuring the given line's equation is in gradient-intercept form?
Signup and view all the answers
Two lines have gradients of 2 and 1/2. What can be said about these lines?
Signup and view all the answers
What is the first step in finding the equation of a line perpendicular to a given line?
Signup and view all the answers
What is the purpose of the point-slope form of a line's equation in finding the equation of a perpendicular line?
Signup and view all the answers
If two lines are perpendicular, what is true about their y-intercepts?
Signup and view all the answers
What is the advantage of using the gradient-intercept form of a line's equation?
Signup and view all the answers
What is the condition for two lines to be perpendicular?
Signup and view all the answers
What is the last step in finding the equation of a perpendicular line?
Signup and view all the answers
What is true about the gradients of two parallel lines?
Signup and view all the answers
What is the purpose of calculating the perpendicular gradient?
Signup and view all the answers