Boyd Rodriguez
01/07/2024 · High School
B. \( y-1=\frac{4}{5}(x-5) \)
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Tutor-Verified Answer
Step-by-step Solution
To rewrite the equation \( y - 1 = \frac{4}{5}(x - 5) \) in slope-intercept form (which is \( y = mx + b \)), we can follow these steps:
1. Distribute \( \frac{4}{5} \) on the right side:
\[
y - 1 = \frac{4}{5}x - \frac{4}{5} \cdot 5
\]
\[
y - 1 = \frac{4}{5}x - 4
\]
2. Add 1 to both sides to isolate \( y \):
\[
y = \frac{4}{5}x - 4 + 1
\]
\[
y = \frac{4}{5}x - 3
\]
Now, the equation in slope-intercept form is:
\[
y = \frac{4}{5}x - 3
\]
This shows that the slope \( m \) is \( \frac{4}{5} \) and the y-intercept \( b \) is \( -3 \).
Quick Answer
The equation in slope-intercept form is \( y = \frac{4}{5}x - 3 \). The slope is \( \frac{4}{5} \) and the y-intercept is \( -3 \).
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