Final answer:
The equation of the line with a slope of -13 passing through the point (1, 13) is y = -13x + 26.
Step-by-step explanation:
To find the equation of the line with slope m = -13 that passes through the point (1, 13), we use the point-slope form of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. Substituting the given point and slope into this formula, we have:
y - 13 = -13(x - 1)
Expanding this equation and solving for y yields the slope-intercept form of the equation of the line, which is y = mx + b. So, we get:
y - 13 = -13x + 13
Add 13 to each side:
y = -13x + 26
This is the equation of the line in slope-intercept form, where the slope is -13, and the y-intercept is 26.