Question

What is the equation of the line with a slope of 3/4 that goes through the point (4,1) in slope-intercept form ?

Answer 1

The slope-point form of a line:

$y-y_0=m(x-x_0)$

We have

$m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1$

Substitute:

$y-1=\dfrac{3}{4}(x-4)$

The slope-intercept form:

$y=mx+b$

Solve for y:

$y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2$

Answer: D.