Question

What is the equation of the line, in slope-intercept form, that goes through the point (5,-6) with m=-3/2?

Answer 1

Start with y = mx + b. Subst. -3/2 for m, -6 for y and 5 for b:

-6 = (-3/2)(5) + b

Mult. all therms by 2: -12 = -15 + b. Then b = 3, and the desired equation is

y = (-3/2)x + 3.

Answer 2

The equation of this line is: y = -3/2x + 1.5.

Since we already have one part of the equation of the line, the slope, we can make the equation with what we have. In slope-intercept form, knowing the value of the slope, the equation becomes:

y = -
`(3)/(2)`x + b

Now we can input the values of x and y from the point we know is on the line. This will allow us to find the value of b. Doing this, we get:

-6 = -
`(3)/(2)` * 5 + b

-6 = -7.5 + b

b = 1.5

Knowing this, the equation of this line is: y = -3/2x + 1.5.