Question

Enter the equation of the line in slope-intercept form. Slope is -1/2, and (-9,4) is on the line. The equation of the line is y=

Answer 1

Answer:

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

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Plug in the slope (m)

We're given that the slope is $\displaystyle-\frac{1}{2}$. In $y=mx+b$, replace m with $\displaystyle-\frac{1}{2}$:

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

2) Determine the y-intercept (b)

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

We're given the point (-9,4). Plug this point into the equation as $(x,y)$ and solve for b:

$4=\displaystyle-\frac{1}{2}(-9)+b\\\\4=\displaystyle\frac{9}{2}+b$

Subtract $\displaystyle\frac{9}{2}$ from both sides to isolate b:

$4-\displaystyle\frac{9}{2}=\displaystyle\frac{9}{2}+b- \displaystyle\frac{9}{2}\\\\\displaystyle-\frac{1}{2} = b$

Therefore, the y-intercept is $\displaystyle-\frac{1}{2}$. Plug this back into $y=\displaystyle-\frac{1}{2}x+b$ as b:

$y=\displaystyle-\frac{1}{2}x+(\displaystyle-\frac{1}{2})\\\\y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}$

I hope this helps!