What is the equation of the line, in slope-intercept form, that goes through the point (-6,-4) with m=-1/2?
For this type of question, you have to use the slope-intercept form equation.
[tex]y=mx+b[/tex]
In the equation, m is the slope and b is the y-intercept.
You are given that m is equal to [tex]-\frac{1}{2}[/tex]. You can put that into the slope-intercept form equation.
[tex]y=-\frac{1}{2}x+b[/tex]
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.
[tex]-4=-\frac{1}{2}(-6)+b[/tex]
Multiply the x and the slope:
[tex]-\frac{1}{2}(-6) = \frac{-6}{-2} =3[/tex]
The answer is positive because a negative number(-) multiplied by a negative number(-) becomes positive(+).
Now add the product to your equation.
[tex]-4=3+b[/tex]
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.
[tex]-4-3=3+b-3 \\ \\ -7=b[/tex]
You have found b, which is -7. Add that to your slope-intercept form equation.
[tex]y=-\frac{1}{2}x-7[/tex]
Your answer is [tex]\bf y=-\frac{1}{2}x-7[/tex]
If you have any questions, feel free to ask in the comments! :)
