Find an equation for the line parallel to y = − 9 x + 5 and goes through the point ( 5 , − 7 ) . Write your answer in the form y = m x + b.

Answer 1

Hi Michelle,

Parallel lines have the same slope. In the slope-intercept form, y = mx + b, the variable m represents the slope and the variable b represents the y-intercept.

For the equation, y = -9 x + 5, the slope is -9. Therefore, the slope of any parallel line will also be -9.

Next, substitute the x and y coordinates for the point provided (5,-7) to determine the y-intercept of the new line:

y = mx + b

y = -9x + b

-7 = -9 •5 + b

-7 = -45 + b

-7 + 45 = -45 + b + 45

38 = b

The equation of the new line in slope-intercept form will be:

y = -9x + 38

Let me know if you have other questions or need any lessons Michelle. Would be happy to help!