Mckenzie Franklin
04/16/2023 · Senior High School
A line has equation \( 3 x+y=15 \) (a) Find the gradient of the line.
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Step-by-step Solution
To find the gradient (slope) of the line given by the equation \( 3x + y = 15 \), we can rearrange the equation into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the gradient.
Starting with the original equation:
\[
3x + y = 15
\]
we can isolate \( y \) by subtracting \( 3x \) from both sides:
\[
y = -3x + 15
\]
Now, the equation is in the form \( y = mx + b \), where \( m = -3 \) and \( b = 15 \).
Thus, the gradient of the line is:
\[
\boxed{-3}
\]
Quick Answer
The gradient of the line is -3.
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