Question
A line intersects the points \[ (8,2) \text { and }(12,-10) \text {. } \] \[ \mathrm{m}=-3 \] Write an equation in point-slope form using the point \( (8,2) \). \( y-[?]=\square(x-\square) \)
Ask by Salazar Cervantes. in the United States
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation in point-slope form using the point \( (8, 2) \) and slope \( m = -3 \) is:
\[
y - 2 = -3(x - 8)
\]
Solution
To write the equation of the line in **point-slope form** using the point \( (8, 2) \) and the slope \( m = -3 \), follow these steps:
**Point-Slope Form:**
\[
y - y_1 = m(x - x_1)
\]
where:
- \( (x_1, y_1) \) is a point on the line.
- \( m \) is the slope of the line.
**Given:**
- Point \( (8, 2) \) where \( x_1 = 8 \) and \( y_1 = 2 \).
- Slope \( m = -3 \).
**Substitute the values into the point-slope form:**
\[
y - 2 = -3(x - 8)
\]
**Final Equation:**
\[
y - 2 = -3(x - 8)
\]
This equation represents the line passing through the points \( (8, 2) \) and \( (12, -10) \) with a slope of \(-3\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To write the equation in point-slope form using the point \( (8,2) \) and the slope \( m = -3 \), you can use the formula: \[ y - y_1 = m(x - x_1) \] Plugging in the values, where \( (x_1, y_1) = (8,2) \) and \( m = -3 \): \[ y - 2 = -3(x - 8) \] So, the equation in point-slope form is: \[ y - 2 = -3(x - 8) \] Now you can confidently express the equation as: \[ y -[2]= -3(x -[8]) \] Which neatly fits the format you're looking for! And voila! You've just found the equation of the line in point-slope form! Isn’t math just a fun way to fashion lines and curves through points?
