Question
Write the equation of a line in slope-intercept form with a slope of 3 that passes through the point (2, 5).
Ask by Grant Chambers. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = 3x - 1 \).
Solution
To find the equation of a line in **slope-intercept form**, which is given by:
\[ y = mx + b \]
where:
- \( m \) is the slope
- \( b \) is the y-intercept
**Given:**
- Slope (\( m \)) = 3
- The line passes through the point (2, 5)
**Steps to find \( b \):**
1. Plug the slope and the coordinates of the given point into the equation:
\[ 5 = 3(2) + b \]
2. Solve for \( b \):
\[ 5 = 6 + b \]
\[ b = 5 - 6 \]
\[ b = -1 \]
**Therefore, the equation of the line is:**
\[ y = 3x - 1 \]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To write the equation of a line in slope-intercept form (y = mx + b), start with the slope (m) of 3. You can use the point (2, 5) to find the y-intercept (b). Plugging in the values into the equation gives us 5 = 3(2) + b. Simplifying this, you get 5 = 6 + b, which leads to b = -1. Therefore, the equation of the line is y = 3x - 1. When working with slope-intercept form, one common mistake is forgetting to adjust the y-intercept after plugging in the coordinates of the point. Always check your calculations to ensure you correctly solve for b!
