In this topic, you will find the equation of a line based on its graph.
In the topic Graphs to Linear Equations, we used the slope-intercept form.
In this topic, we use the point-slope form:

y - y₁ = m(x - x₁ )     where m is the slope and (x₁, y₁) is a point on the line

1. Find the slope of the line, m.
2. Find a point on the line, (x₁, y₁).
3. Plug m, x₁, and y₁ into the equation y - y₁ = m(x - x₁ ).

Example 1:

Write the equation in point slope format, y-y1=m(x-x1), then convert into slope intercept form, y=mx+b.

Point Slope Equation: Slope Intercept Equation:

Point-slope equation:

Step 1: Find the slope, m.
Let's pick the two points (0, 0) and (4, -2) on the line to find the slope.

m

=

0 - (-2)     0 - 4

=

2  -4

=

1  -2

Step 2: Find a point on the line, (x₁, y₁).
We can use the point given (4, -2).

Step 3: Plug m, x₁, and y₁ into the equation.

y - y1	=	m (	x - x1 )
y - (-2)	=	-1   2	(x - 4)
y + 2	=	-1   2	(x - 4)

Slope-intercept equation:

To convert a point-slope equation to a slope-intercept equation, use algebra to solve for y.

y + 2	=	-1   2	(x - 4)
y + 2	=	-x   2	+ 2
y	=	-x   2

Point Slope Equation:
Slope Intercept Equation: