Algebra 1 Practice - Write an Equation in Slope-Intercept Form (Example 2)
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Sure, here's how to write an equation in slope-intercept form directly, given information about the slope, points, or y-intercepts:
1. *Using Slope and Y-Intercept*
If you have the slope \( m \) and the y-intercept \( b \), you can directly write the equation in slope-intercept form:
\[ y = mx + b \]
*Example:*
Slope (\( m \)) = 3
Y-intercept (\( b \)) = -2
The equation is:
\[ y = 3x - 2 \]
2. *Using a Point and the Slope*
If you have the slope \( m \) and a point \((x_1, y_1)\), you can find the y-intercept \( b \) and then write the equation in slope-intercept form.
1. *Calculate the y-intercept \( b \):*
Rearrange the slope-intercept form \( y = mx + b \) to solve for \( b \):
\[ b = y - mx \]
Substitute the coordinates of the point \((x_1, y_1)\) and the given slope \( m \):
\[ b = y_1 - m x_1 \]
2. *Write the equation:*
Substitute the slope \( m \) and y-intercept \( b \) into the slope-intercept form:
\[ y = mx + b \]
*Example:*
Slope (\( m \)) = 4
Point = (2, 5)
Calculate \( b \):
\[ b = 5 - 4 \cdot 2 \]
\[ b = 5 - 8 \]
\[ b = -3 \]
The equation is:
\[ y = 4x - 3 \]
3. *Using Two Points*
If you have two points \((x_1, y_1)\) and \((x_2, y_2)\), follow these steps:
1. *Calculate the slope \( m \):*
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
2. *Find the y-intercept \( b \):*
Substitute one of the points and the slope into the equation \( y = mx + b \) to solve for \( b \):
\[ b = y - mx \]
Use one of the given points \((x_1, y_1)\):
\[ b = y_1 - m x_1 \]
3. *Write the equation:*
Substitute the slope \( m \) and y-intercept \( b \) into the slope-intercept form:
\[ y = mx + b \]
*Example:*
Points = (1, 3) and (4, 11)
Calculate the slope \( m \):
\[ m = \frac{11 - 3}{4 - 1} = \frac{8}{3} \]
Find the y-intercept \( b \):
\[ b = 3 - \frac{8}{3} \cdot 1 \]
\[ b = 3 - \frac{8}{3} \]
\[ b = \frac{9}{3} - \frac{8}{3} \]
\[ b = \frac{1}{3} \]
The equation is:
\[ y = \frac{8}{3}x + \frac{1}{3} \]
Using these methods, you can determine the slope-intercept form of a linear equation given the necessary information.
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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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