Graphing Linear Equations Quiz

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.