To find the equation of a line in slope-intercept form (y = mx + b), you need the slope (m) and the y-intercept (b).
You've mentioned that the slope (m) is -2 and that the line passes through the point (6, 13).
We can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the point on the line. Plugging in the values:
- \( m = -2 \)
- \( x_1 = 6 \)
- \( y_1 = 13 \)
The equation becomes:
\[ y - 13 = -2(x - 6) \]
Now, we'll simplify the equation:
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Distribute the slope (-2): \[ y - 13 = -2x + 12 \]
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Add 13 to both sides to isolate \( y \): \[ y = -2x + 12 + 13 \] \[ y = -2x + 25 \]
So, the equation of the line in slope-intercept form is:
\[ y = -2x + 25 \]
Thus, your final answer is: \[ y = -2x + 25 \]