Mcdonald Brewer
01/20/2024 · High School
(a) Write the equation of the line in slope-intercept form. (b) Write the equation of the line in the form \( A x+B y=C \). \( m=\frac{4}{5}, y \)-intercept \( (0,8) \)
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Tutor-Verified Answer
Step-by-step Solution
To find the equation of the line given the slope \( m = \frac{4}{5} \) and the \( y \)-intercept \( (0, 8) \), we can follow these steps:
### (a) Slope-Intercept Form
The slope-intercept form of a line is given by the equation:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the \( y \)-intercept.
Given:
- \( m = \frac{4}{5} \)
- \( b = 8 \)
Substituting these values into the equation:
\[
y = \frac{4}{5}x + 8
\]
### (b) Standard Form \( Ax + By = C \)
To convert the slope-intercept form \( y = \frac{4}{5}x + 8 \) into standard form \( Ax + By = C \), we can follow these steps:
1. Start with the slope-intercept form:
\[
y = \frac{4}{5}x + 8
\]
2. Multiply every term by 5 to eliminate the fraction:
\[
5y = 4x + 40
\]
3. Rearrange the equation to get it into the standard form:
\[
-4x + 5y = 40
\]
4. To write it in the standard form with \( A \) as a positive integer, we can multiply the entire equation by -1:
\[
4x - 5y = -40
\]
Thus, the equations are:
- (a) \( y = \frac{4}{5}x + 8 \)
- (b) \( 4x - 5y = -40 \)
Quick Answer
(a) \( y = \frac{4}{5}x + 8 \)
(b) \( 4x - 5y = -40 \)
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