Problem

A line passes through the point $(-10,-7)$ and has a slope of $-\frac{1}{2}$. Write an equation in slope-intercept form for this line.

Answer

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Answer

\(\boxed{y = -\frac{1}{2}x - 12}\) is the final answer.

Steps

Step 1 ：The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：We know the slope \(m\) is \(-\frac{1}{2}\) and we have a point \((-10,-7)\) that the line passes through.

Step 3 ：We can substitute these values into the equation to solve for \(b\).

Step 4 ：\(m = -0.5\)

Step 5 ：\(b = -12.0\)

Step 6 ：Now that we have the y-intercept \(b\), we can write the equation of the line in slope-intercept form.

Step 7 ：\(\boxed{y = -\frac{1}{2}x - 12}\) is the final answer.

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