Question

A line with a slope of 3/2 passes through (4,-1). Write the equation.

Answer 1

Hey there!

We're going to write the equation for this line in slope-intercept form, y = mx+b, where m is the slope and b is the y-intercept. In order to write it in this form, as stated in the name, we need the slope and y-intercept. Since we have the slope given, we can use the points we have and set up that equation with the given slope to solve for b. We'll use the x and y values and throw them into the equation. We have:

-1 = 3/2(4) + b
-1 = 12/2 + b
-1 = 6 + 6
-6 = b

Now, since we have our slope and y-intercept, we can write our equation with these two values:

y = 3/2x - 6

Hope this helps!

Answer 2

we know that

the equation of the line in the form point-slope is equal to

$y-y1=m*(x-x1)$

in this problem we have

$point(4,-1)\\\\m=\frac{3}{2}$

Substitute the values

$y+1=\frac{3}{2}*(x-4)$

$y=\frac{3}{2}x-6-1\\\\y=\frac{3}{2}x-7$

therefore

the answer is

$y=\frac{3}{2}x-7$