Question

Write the equation in slope-intercept form and then graph the equation that passes through (5, -7) and is parallel to to y = −4x + 3

Answer 1

The slope-intercept form is:

$y=mx+b$

Where m is the slope and b is the intercept.

For two lines to be parallel they have to have the same slope. So a line parallel to

$y=-4x+3$

Has m = -4. So until now we have this equation:

$y=-4x+b$

To find the intercept b we use the given point (5,-7). We just have to replace these values of x and y into the equation above and solve for b:

$\begin{gathered} -7=-4\cdot5+b \\ -7+20=b \\ 13=b \end{gathered}$

So there we have the complete equation of the asked line:

$y=-4x+13$

And the graph is: