Question

What is the slope-intercept form of the equation y-7=5/2(x+4)?

y-2=-(5/2) (x+2)
y+7=-x+5/2
y=-(4/7)+2
y=(-(5/2)x)-3

Answer 1

The first step is to note the particular forms of point-slope versus slope-intercept.

POINT-SLOPE: y - y1 = m(x - x1)
SLOPE-INTERCEPT: y = mx + b

You have that y - 7 = (5/2)(x + 4)

This way, you know that m = (5/2), x1 = -4, and y1 = 7.

First, plug in the known slope (m).

y = (5/2)x + b

Now you need to find the value of b. The easiest way to do this is simply to plug in values for x and y and solve for b. This is very easy since we now have values for x and y: (-4, 7).

7 = (5/2)(-4) + b
7 = -10 + b
b = 17

Voila, we have a value for b. Simply plug that into your slope-intercept formula, and you're done! We have now...

y = (5/2)x + 17

Unfortunately, I cannot really decipher some of the answers you have given as choices, so I can't tell you with 100% accuracy which answer is the right one. I can tell you with most certainty that the slope-intercept that I've given you is probably correct.