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01/19/2023 · High School
A line passes through the point \( (3,-8) \) and has a slope of -7
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Step-by-step Solution
To find the equation of a line that passes through the point \( (3, -8) \) with a slope of \( -7 \), we can use the point-slope form of the equation of a line, 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.
In this case, \( (x_1, y_1) = (3, -8) \) and \( m = -7 \). Plugging these values into the point-slope form, we get:
\[
y - (-8) = -7(x - 3)
\]
This simplifies to:
\[
y + 8 = -7(x - 3)
\]
Next, we can distribute the \( -7 \):
\[
y + 8 = -7x + 21
\]
Now, we isolate \( y \) by subtracting \( 8 \) from both sides:
\[
y = -7x + 21 - 8
\]
This simplifies to:
\[
y = -7x + 13
\]
Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = -7x + 13}
\]
Quick Answer
The equation of the line is \( y = -7x + 13 \).
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