Answer:
The equation of the line that is perpendicular to y = -5x + 7 and has a y-intercept of -8 is:
y = 1/5x - 8
Explanation:
The given line has the equation y = -5x + 7, where the slope (m) is -5. To find a line that is perpendicular, we need to take the negative reciprocal of the slope. The negative reciprocal of -5 is 1/5.
The y-intercept of the perpendicular line is given as -8, which corresponds to the point (0, -8).
Use the point-slope form of a line equation to find the equation of the perpendicular line:
y - y₁ = m(x - x₁)
Substituting the values:
y - (-8) = (1/5)(x - 0)
Simplify:
y + 8 = 1/5x
To isolate y, subtract 8 from both sides of the equation:
y = 1/5x - 8
So, the equation of the line that is perpendicular to y = -5x + 7 and has a y-intercept of -8 is y = 1/5x - 8.