Question
Write an equation of the line with the given slope, \( m \), and \( y \)-intercept \( m=-5, b=-\frac{1}{10} \) The equation is
Ask by Haynes Gibbs. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = -5x - \frac{1}{10} \).
Solution
**Step 1:** Recall the slope-intercept form of a line:
\[
y = mx + b
\]
**Step 2:** Substitute the given slope \( m = -5 \) and \( y \)-intercept \( b = -\frac{1}{10} \) into the formula:
\[
y = -5x -\frac{1}{10}
\]
Thus, the equation of the line is:
\[
y = -5x -\frac{1}{10}
\]
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Simplify this solution Beyond the Answer
The equation of a line in slope-intercept form is given by \( y = mx + b \). Given that the slope \( m = -5 \) and the \( y \)-intercept \( b = -\frac{1}{10} \), you can substitute these values into the equation. So, the line's equation will be: \[ y = -5x - \frac{1}{10} \] To visualize this, imagine you’re starting at the point \((0, -\frac{1}{10})\) on the y-axis and moving downward steeply to the left due to the negative slope—every time you move one unit to the right, you’ll move five units down!
