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If we take the equation of a line and solve it for y we get the slope-intercept form for the equation of a line.
Definition
Slope-Intercept Form for the Equation of a Line
The slope-intercept form for the equation of a line with slope m and
y-intercept (0, b) is: y = mx + b
Example 1
Find the equation of a line in slope-intercept form that has slope m = 2 and y-intercept (0,
-3).
| Solution |
y = mx + b |
| The point (0, -3) has the form (0, b). So, b is -3. |
| Thus, replace m with 2 and b with -3. |
y = 2x - 3 |
| The slope-intercept form for the equation of this line is
y = 2x - 3 |
Example 2
Write the equation 4x - 3y = 12 in slope-intercept form.
| Solution |
4x - 3y |
= 12 |
| Solve the given equation for y.
|
| Subtract 4x from both sides. |
-3y |
= -4x + 12 |
| Divide both sides by -3. |
 |
 |
| Simplify. |
y |
 |
So, the equation in slope-intercept form is
 .
The slope of this line is
 and the y-intercept is (0,
-4).
Example 3
Find the slope-intercept form for the equation of the line that passes
through the points (-6, 1) and (2, 5).Solution
First, we need to find the slope, m.
In the slope formula, let (x1, y1) = (-6, 1) and (x2, y2)
= (2, 5).
So, the slope is
 .
Note:
You can use either point (x1, y1) and (x2, y2).
| Next, use the point-slope formula.
|
y - y1 |
= m(x - x1) |
Let (x1, y1) = (-6, 1) and
 |
y - 1 |
 |
| y - 1 |
 |
| Then, solve for y.
|
Distribute
 on the right side.
|
y - 1 |
 |
| Add 1 to both sides. |
y |
 |
So, the slope-intercept form for the equation
Note:
You can also write
in standard
form, Ax + By = C. To do this, subtract
 from both sides to
get
Now, multiply both sides by 2 to get:
-x + 2y = 8
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