Question

What is the slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4`?

Answer 1

The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4 is $y = \frac{3}{4}x + \frac{-31}{4}$

Solution:

Given that line passes through (5, -4)

Slope "m" = $\frac{3}{4}$

We have to find the slope intercept form

The slope intercept form is given as:

y = mx + b  ---- eqn1

where "m" is the slope of the line and "b" is the y-intercept

Here in this sum m = $\frac{3}{4}$

Calculating y-intercept:

Substitute (x, y) = (5, -4) and "m" value in eqn 1, we get

$\begin{array}{l}{-4=\frac{3}{4}(5)+b} \\\\ {-4=\frac{15+4 b}{4}} \\\\ {-16=15+4 b} \\\\ {4 b=-31} \\\\ {b=\frac{-31}{4}}\end{array}$

Now eqn 1 becomes,

$y = \frac{3}{4}x + \frac{-31}{4}$

Hence the slope intercept form is $y = \frac{3}{4}x + \frac{-31}{4}$

Answer 2

Answer:

y = 3/4x -31/4

Step-by-step explanation: