Question
If one point on a line is \( (8,-7) \) and the line's slope is -6 , find the \( y \)-intercept. The \( y \)-intercept is \( \square \). (Type an integer or a simplified fraction.)
Ask by Ayala Hobbs. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The y-intercept is 41.
Solution
We know the point (8, -7) is on the line and the slope is -6. Using the slope-intercept form of a line, y = mx + b, substitute the point and the slope to solve for b.
Step 1: Plug in the point (8, -7) and slope m = -6.
-7 = -6(8) + b
Step 2: Simplify the equation.
-7 = -48 + b
Step 3: Solve for b by adding 48 to both sides.
-7 + 48 = b
41 = b
Therefore, the y-intercept is 41.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the \( y \)-intercept, we can use the point-slope form of a line equation, which is given by \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope. Plugging in the values, we have: \[ y - (-7) = -6(x - 8) \] This simplifies to: \[ y + 7 = -6x + 48 \] Now, let's isolate \( y \): \[ y = -6x + 48 - 7 \] \[ y = -6x + 41 \] In this slope-intercept form \( y = mx + b \), the \( y \)-intercept \( b \) is 41. The \( y \)-intercept is \( 41 \).
