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Graphs to Linear Equations 2


For this topic, you need to know the slope-intercept form.
To review the Graphs to Linear Equations topic, see here.

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
To find the equation of a line, follow these steps:
  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:

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