Finding Linear Equations From Graphs Practice Questions

To review these concepts, go to Finding Linear Equations From Graphs Study Guide.

Finding Linear Equations From Graphs Practice Questions

Problems

Practice 1

Find the equation of the line on each graph.

Practice 2

Determine whether the points (20,2) and (–20,10) fall on each of the following graphed lines below.

Solutions

Practice 1

1. To find the equation of the line, begin by finding the slope using any two points on the line. When x = 1, y = –4, and when x = 2, y = –3. Use these points to find the slope: . The y-intercept can be found right on the graph. The line crosses the y-axis where y = –5, which means that –5 is the y-intercept. This is the graph of the equation y = x – 5.

2. To find the equation of the line, begin by finding the slope using any two points on the line. When x = –4, y = 6, and when x = –3, y = 0. Use these points to find the slope: To find the y-intercept, use the slope, any point on the graph, and the equation y = mx + b. Using the point (–3,0):

   0 = –6(–3) + b

   0 = 18 + b

   –18 = b

   This is the graph of the equation y = –6x – 18.

3. To find the equation of the line, begin by finding the slope using any two points on the line. When x = –5, y = 0, and when x = 0, y = 4. Use these points to find the slope: The y-intercept can be found right on the graph. The line crosses the y-axis where y = 4, which means that 4 is the y-intercept. This is the graph of the equation

4. To find the equation of the line, begin by finding the slope using any two points on the line. When x = 0, y = 7, and when x = 1, y = 7. In fact, for any value of x, = 7. Use these points to find the slope: The slope of this equation is 0, which means that x will not be part of the equation. The y-intercept can be found right on the graph. The line crosses the y-axis where y = 7, which means that 7 is the y-intercept. This is the graph of the equation y = 7.

Practice 2

1. It is impossible to tell just by looking at the graph if (20,2) and (–20,10) are points on this line. Find the equation of the line first. Use any two points, such as (0,6) and (5,5) to find the slope: The line crosses the y-axis where y = 6, which means that 6 is the y-intercept. This is the graph of the equation

   Check to see if (20,2) falls on the line by substituting 20 for x and 2 for y:

   

   2 = –4 + 6 ?

   2 = 2

   The equation holds true, so (20, 2) is on the line . Check (–20, 10):

   

   10 = 4 + 6 ?

   10 = 10

   The equation holds true again, so (–20,10) is also on the line

2. It is impossible to tell just by looking at the graph if (20, 2) and (–20, 10) are points on this line. Find the equation of the line first. Use any two points, such as (0,–3) and (4,–2) to find the slope: . The line crosses the y-axis where y = –3, which means that –3 is the y-intercept. This is the graph of the equation

   Check to see if (20, 2) falls on the line by substituting 20 for x and 2 for y:

   

   2 = 5 – 3 ?

   2 = 2

   The equation holds true, so (20,2) is on the line Check (–20,10):

   

   10 = –5 –3 ?

   10 ≠ –8

   The equation does not hold true, so (–20,10) is not on the line