Question

what is the equation of the line, in slope-intercept form, that goes through the point (-6,-4) with m=-1/2

Answer 1

QUESTION

What is the equation of the line, in slope-intercept form, that goes through the point (-6,-4) with m=-1/2?

ANSWER AND EXPLANATION

For this type of question, you have to use the slope-intercept form equation.

$y=mx+b$

In the equation, m is the slope and b is the y-intercept.

You are given that m is equal to $-\frac{1}{2}$. You can put that into the slope-intercept form equation.

$y=-\frac{1}{2}x+b$

Now you need to find b. To do that, you can substitute y and x with the x and y in the ordered pair given.

The y in the ordered pair is -4. Substitute y with -4 in the equation you have. The x is -6. Substitute x with -6 in the equation.

$-4=-\frac{1}{2}(-6)+b$

Multiply the x and the slope:

$-\frac{1}{2}(-6) = \frac{-6}{-2} =3$

The answer is positive because a negative number(-) multiplied by a negative number(-) becomes positive(+).

Now add the product to your equation.

$-4=3+b$

To leave b alone, subtract 3 from both sides. You need to subtract because to cancel out everything with b, you have to do the opposite of it.

$-4-3=3+b-3 \\ \\ -7=b$

You have found b, which is -7. Add that to your slope-intercept form equation.

$y=-\frac{1}{2}x-7$

Your answer is $\bf y=-\frac{1}{2}x-7$

If you have any questions, feel free to ask in the comments! :)