Question

Find the equation of the line, in slope-intercept form, through (-4, 6)and parallel to y=-3x + 4. (Show work) (3 pts)

Answer 1

The given equation is

`y=-3x+4`

Notice that this equation represents a line in slope-intercept form, where its slope is -3.

Now, we have to find a new line parallel to the one above, which means the slope of the new line is also 3 because parallel lines have equal slopes.

Then, we use the given points (-4,6) and the slope -3 to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-6=-3(x-(-4)) \\ y-6=-3x-12 \\ y=-3x-12+6 \\ y=-3x-6 \end{gathered}`

Therefore, the equation of the parallel line is y = -3x - 6.