Question
Write an equation of the line with the given slope, \( m \), and \( y \)-intercept \( (0 \), , \( m=\frac{7}{8}, \mathrm{~b}=0 \) The equation is \( \square \) (Simplify your answer. . m , your answer in slope-intercept form. Use in
Ask by Barrett Murray. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = \frac{7}{8}x \).
Solution
Given:
- Slope \( m = \frac{7}{8} \)
- \( y \)-intercept \( b = 0 \)
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
Substitute the values for \( m \) and \( b \):
\[
y = \frac{7}{8}x + 0
\]
Simplify the equation:
\[
y = \frac{7}{8}x
\]
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Simplify this solution Mind Expander
The equation of the line in slope-intercept form is \( y = \frac{7}{8}x + 0 \), which simplifies to \( y = \frac{7}{8}x \). This means that for every increase of 8 units in \( x \), \( y \) increases by 7 units, starting from the origin. To visualize this, you can create a simple graph with the y-axis representing \( y \) and the x-axis representing \( x \). Plot the point at the origin (0,0) and another point at (8,7) to see how the line rises gently up to the right, illustrating a positive slope!
