# Linear Equations in Point-Slope Form

## Key Questions

1) point-slope form
2) slope intercept form

#### Explanation:

1) y−b=m(x−a)
m = slope
(a, b) A point that the line passes through

2) $y = m x + b$
m = slope
b = y-intercept

Explanation below:

#### Explanation:

Let's use this example from http://www.purplemath.com/modules/strtlneq2.htm to help you understand how to graph point-slope form equations:

$m = 4$, x_1 = –1, and y_1 = –6 are given.

Formula:

y – y_1 = m(x – x_1)

y – (–6) = (4)(x – (–1))

Simplify. Two negatives make a positive:

$y + 6 = 4 \left(x + 1\right)$

Distribute 4 to x and 1. Simplify.

$y + 6 = 4 x + 4$

Subtract 6 from both sides.

y = 4x – 2

graph{y=4x-2 [-12.66, 12.65, -7.7, 4.96]}

http://www.purplemath.com/modules/strtlneq2.htm

• To find the equation of a line having a point $P \left({x}_{p} , {y}_{p}\right)$ and with the slope $m$, this formula can be used:

$y - {y}_{p} = m \left(x - {x}_{p}\right)$.

E.G.:

Find the line that passes from P(2,-3) with the slope of 4:

$y + 3 = 4 \left(x - 2\right) \Rightarrow y = 4 x - 11$.

graph{4x-11 [-10, 10, -5, 5]}.