Question
Which of the following is the equation of the line that has a slope of -3 and passes through the point \( (-2,6) \) ?
Ask by Bowen French. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = -3x \).
Solution
We begin with the point-slope form of a line:
\[
y - y_1 = m(x - x_1)
\]
Substitute the given slope \( m = -3 \) and point \( (x_1, y_1) = (-2, 6) \):
\[
y - 6 = -3(x - (-2))
\]
Simplify the expression inside the parentheses:
\[
y - 6 = -3(x + 2)
\]
Distribute \(-3\):
\[
y - 6 = -3x - 6
\]
Add 6 to both sides to solve for \( y \):
\[
y = -3x - 6 + 6
\]
\[
y = -3x
\]
Thus, the equation of the line is:
\[
y = -3x
\]
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Simplify this solution The Deep Dive
To find the equation of the line, you can use the point-slope form: \(y - y_1 = m(x - x_1)\). Here, \(m\) is the slope, and \((x_1, y_1)\) is the given point. Plugging in your values: \(y - 6 = -3(x + 2)\). Simplifying this gives the equation \(y = -3x + 12\). Voilà! You've got yourself an equation! Now, imagine you're plotting it! The slope of -3 means that for every step you take to the right (along the x-axis), you’ll step down three units (along the y-axis). Connecting the points will give you a straight line, starting at that point (-2,6) and moving downwards as you go right.
