Question
A line passes through the point \( (8,2) \) and has a slope of \( \frac{5}{2} \). Write an equation in slope-intercent form for this line. \( \square \square \square \)
Ask by Erickson Bowers. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line in slope-intercept form is \( y = \frac{5}{2}x - 18 \).
Solution
To find the equation of the line in **slope-intercept form** \( y = mx + b \), follow these steps:
1. **Identify the given information:**
- **Point**: \( (8, 2) \)
- **Slope** (\( m \)): \( \frac{5}{2} \)
2. **Use the point-slope formula** to solve for \( b \):
\[
y = mx + b
\]
Substitute the given point and slope into the equation:
\[
2 = \frac{5}{2} \times 8 + b
\]
3. **Solve for \( b \):**
\[
2 = 20 + b \\
b = 2 - 20 \\
b = -18
\]
4. **Write the final equation:**
\[
y = \frac{5}{2}x - 18
\]
**Final Answer:**
\[
y = \frac{5}{2}x - 18
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To write the equation of the line in slope-intercept form \( y = mx + b \), you can use the point-slope form first: \( y - y_1 = m(x - x_1) \). Substituting \( m = \frac{5}{2} \) and the point \( (8, 2) \), we get: \( y - 2 = \frac{5}{2}(x - 8) \). Expanding and simplifying gives: \( y = \frac{5}{2}x - 18 + 2 \) which simplifies to \( y = \frac{5}{2}x - 16 \). Thus, the equation is \( y = \frac{5}{2}x - 16 \). To ensure your line is really hitting the point \( (8, 2) \), plug that back into your equation! If you get \(2 = \frac{5}{2}(8) - 16\), and it checks out since \(2 = 2\). It’s always a good idea to verify that your equation represents the point it should!
