Question

Find the equation of the line through (4,1/2) and has a slope of -3. Write your answer in general form.

Answer 1

ANSWER

y = -3x + 25/2

EXPLANATION

The slope-intercept form of the equation of a line is:

$y=mx+b$

Where m is the slope and b is the y-intercept.

In this problem we're given the slope of the line:

$y=-3x+b$

And we have to find the y-intercept to complete the equation. We know that the line passes through point (4, 1/2). Replace x and y by this point:

$\frac{1}{2}=-3\cdot4+b$

And solve for b:

$\begin{gathered} \frac{1}{2}=-12+b \\ b=\frac{1}{2}+12 \\ b=\frac{25}{2} \end{gathered}$

The equation is:

$y=-3x+\frac{25}{2}$