Answer:
y = (-1/4)x + 2
Explanation:
The given line has a slope of 4 since it is in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of a line perpendicular to this line, we use the fact that the product of the slopes of perpendicular lines is -1. Therefore, the slope of the new line is -1/4.
We can now use the point-slope form of a line to find the equation of the line passing through the point (-8,4) with slope -1/4. The point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values, we get:
y - 4 = (-1/4)(x - (-8))
Simplifying this equation, we get:
y - 4 = (-1/4)x - 2
Adding 4 to both sides, we get:
y = (-1/4)x + 2
Therefore, the equation of the line that is perpendicular to y= 4x + 8 and passes through (-8,4) is y = (-1/4)x + 2.