Questions: A line has a slope of -1/2 and passes through the point (-12,0). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Solution Steps

To write the equation of a line in slope-intercept form \( y = mx + b \), we need the slope \( m \) and the y-intercept \( b \). We are given the slope \( m = -\frac{1}{2} \) and a point \((-12, 0)\) through which the line passes. We can use the point-slope form of the equation \( y - y_1 = m(x - x_1) \) to find \( b \).

1. Substitute the given point and slope into the point-slope form to find the y-intercept \( b \).
2. Rewrite the equation in slope-intercept form \( y = mx + b \).

We are given the slope \( m = -\frac{1}{2} \) and a point \((-12, 0)\) through which the line passes.

Using the point-slope form of the equation \( y - y_1 = m(x - x_1) \), we can find the y-intercept \( b \).

\[ y - 0 = -\frac{1}{2}(x + 12) \]

Simplifying, we get:

\[ y = -\frac{1}{2}x - 6 \]

Thus, the y-intercept \( b \) is \(-6\).

Now that we have the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = -6 \), we can write the equation of the line in slope-intercept form \( y = mx + b \).

\[ y = -\frac{1}{2}x - 6 \]

Final Answer