Relationship Between Variables in the Equation of a Line Practice Questions

To review these concepts, go to Relationship Between Variables in the Equation of a Line Study Guide.

Relationship Between Variables in the Equation of a Line Practice Questions

Problems

Practice 1

Find the equation that was used to build each table.

Practice 2

Find the missing value in each table.

Solutions

Practice 1

1. First, find the slope. Take the difference between the first two y values in the table and divide it by the difference between the first two x values in the table: The slope of the line is 5. Next, find the y-intercept using the equation y = mx + b. Substitute 5, the slope of the line, for m. Substitute the values of x and y from the first row of the table, and solve for b, the y-intercept:

   5 = 5(1) + b

   5 = 5 + b

   0 = b

   The slope of the line is 5 and the y-intercept is 0. The equation of this line is y = 5x + 0, or y = 5x.

2. First, find the slope. Take the difference between the first two y values in the table and divide it by the difference between the first two x values in the table: The slope of the line is –1. Next, find the y-intercept using the equation y = mx + b. Substitute –1, the slope of the line, for m. Substitute the values of x and y from the third row of the table, and solve for b, the y-intercept:

   2 = –1(0) + b

   2 = 0 + b

   2 = b

   The slope of the line is –1 and the y-intercept is 2. The equation of this line is y = –1x + 2, or y = –x+ 2.

3. First, find the slope. Take the difference between the first two y values in the table and divide it by the difference between the first two x values in the table: The slope of the line is 3. Next, find the y-intercept using the equation y = mx + b. Substitute 3, the slope of the line, for m. Substitute the values of x and y from the first row of the table, and solve for b, the y-intercept:

   –1 = 3(2) + b

   –1 = 6 + b

   –7 = b

   The slope of the line is 3 and the y-intercept is –7. The equation of this line is y = 3x – 7.

4. First, find the slope. Take the difference between the first two y values in the table and divide it by the difference between the first two x values in the table: The slope of the line is Next, find the y-intercept using the equation y = mx + b. Substitute the slope of the line, for m. Substitute the values of x and y from the third row of the table, and solve for b, the y-intercept:

   

   4 = 1 + b

   3 = b

   The slope of the line is 12 and the y-intercept is 3. The equation of this line is

Practice 2

1. First, find the equation that was used to build the table. Use the first two rows of the table to find the slope: Use the first row of the table and the equation y = mx + b to find the y-intercept of the equation. Remember: m is the slope and b is the y-intercept:

   –8 = 1(1) + b

   –8 = 1 + b

   –9 = b

   The equation for this table is y = x – 9. To find the value of y when x = 5, substitute 5 for x in the equation and solve for y:

   y = (5) – 9

   y = 5 – 9

   y = –4

   The missing value in the table is –4.

2. First, find the equation that was used to build the table. Use the first two rows of the table to find the slope: Use the fourth row of the table and the equation y = mx + b to find the y-intercept of the equation:

   –3 = –8(1) + b

   –3 = –8 + b

   5 = b

   The equation for this table is y = –8x + 5. To find the value of y when x = 0, substitute 0 for x in the equation and solve for y:

   y = –8(0) + 5

   y = 0 + 5

   y = 5

   The missing value in the table is 5.

3. First, find the equation that was used to build the table. Use the last two rows of the table to find the slope: Use the fourth row of the table and the equation y = mx + b to find the y-intercept of the equation:

   –3 = 4(3) + b

   –3 = 12 + b

   –15 = b

   The equation for this table is y = 4x – 15. To find the value of x when y = –11,substitute –11 for y in the equation and solve for x:

   –11 = 4x – 15

   4 = 4x

   1 = x

   The missing value in the table is 1.

4. First, find the equation that was used to build the table. Use the first two rows of the table to find the slope: Use the second row of the table and the equation y = mx + b to find the y-intercept of the equation:

   1 = –14(–8) + b

   1 = 2 + b

   –1 = b

   The equation for this table is To find the value of y when x = 24, substitute 24 for x in the equation and solve for y:

   

   y = –6 – 1

   y = –7

   The missing value in the table is –7.