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Questions and Answers
What is the value of $f(x)$ when $x = 0$ for a line with a y-intercept of 3?
What is the value of $f(x)$ when $x = 0$ for a line with a y-intercept of 3?
What is the slope of the line that passes through the points (1, 2) and (3, 6)?
What is the slope of the line that passes through the points (1, 2) and (3, 6)?
Which line has a slope of zero?
Which line has a slope of zero?
For the equation $y - 3 = 2(x + 5)$, what is the y-intercept?
For the equation $y - 3 = 2(x + 5)$, what is the y-intercept?
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What is the equation of the line that is perpendicular to the line $y = 2x + 1$ and passes through the point (2, 3)?
What is the equation of the line that is perpendicular to the line $y = 2x + 1$ and passes through the point (2, 3)?
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Which point lies on the line defined by the equation $4x - 5y + 12 = -8$?
Which point lies on the line defined by the equation $4x - 5y + 12 = -8$?
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What is the x-intercept of the line represented by the equation $-2x + 5y = 12$?
What is the x-intercept of the line represented by the equation $-2x + 5y = 12$?
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Which equation represents a horizontal line?
Which equation represents a horizontal line?
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Study Notes
Graphing Linear Equations
- The y-intercept of a line is the point where the line crosses the y-axis.
- The x-intercept of a line is the point where the line crosses the x-axis.
- The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
- The slope of a line can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).
- The equation of a line can be written in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- The equation of a line can also be written in point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
- Parallel lines have the same slope.
- Perpendicular lines have slopes that are negative reciprocals of each other.
- The x-intercept of a line is the point where y = 0.
- The y-intercept of a line is the point where x = 0.
- A horizontal line has a slope of 0.
- A vertical line has an undefined slope.
- To find the equation of a line, you need to know either the slope and a point on the line or two points on the line.
- The equation of a line can be used to find the value of y for a given value of x or vice versa.
- The graph of a linear equation is a straight line.
- The equation of a line can be used to model real-world situations.
Finding the Equation of a Line
- To find the equation of the line find the slope of the line.
- Use the slope and one of the points from the line to write the equation in point-slope form.
- Simplify the equation.
Identifying Points on a Line
- To determine if a point lies on the line, substitute the x and y coordinates of the point into the equation of the line.
- If the equation is true, then the point lies on the line.
- If the equation is false, then the point does not lie on the line.
Parallel and Perpendicular Lines
- The slope of a line parallel to a given line is the same as the slope of the given line.
- The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
- To find the equation of a line that is parallel or perpendicular to a given line, you need to know the slope of the given line and a point on the line.
Applications of Linear Equations
- Linear equations are used in many real-world applications, such as modeling the relationship between two variables.
- For example, linear equations can be used to model the relationship between the price of a product and the quantity sold.
- Linear equations can also be used to model the relationship between the amount of time spent studying and the grade received on a test.
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Description
Test your knowledge on graphing linear equations with this quiz. It covers key concepts such as slope, intercepts, and different forms of linear equations. Answer questions related to parallel and perpendicular lines along with their properties.
