Question

-Determine the equation of the line that passes through the point (9, -42)and is parallel to the line y = -5x + 1.Enter your answer in slope-intercept form.Pls see picture

Answer 1

Two parallel lines have the same slope. Given the equation of one of the lines, you can determine the slope of the other line:

`y=-5x+1`

The slope of the line is the coefficient of the x-term, in this case, that coefficient is -5. Then the slope of both parallel lines is m= -5.

The line you have to find must cross through the point (9,-42). Using the point-slope form you can determine the equation of the parallel line:

`y-y_1=m(x-x_1)`

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line:

`\begin{gathered} y-(-42)=-5(x-9) \\ y+42=-5(x-9) \end{gathered}`

To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:

`\begin{gathered} y+42=(-5)\cdot x+(-5)\cdot(-9) \\ y+42=-5x+45 \end{gathered}`

Subtract 42 to both sides of the expression to pass the term to the right side of the equal sign:

`\begin{gathered} y+42-42=-5x+45-42 \\ y=-5x+3 \end{gathered}`

The equation of the line is y= -5x + 3