Math Practice Online > free > lessons > Florida > 9th grade > Graphs to Linear Equations 2

Here are some tips for Graphs to Linear Equations 2, which aligns with Florida state standards:

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:

Copyright Accurate Learning Systems Corporation 2008.