A line has x-intercept (5, 0) and is perpendicular to the line 2x + 8y = 10. Find the y-intercept of the line.

Answer 1

your given line of 2x + 8y = 10 has slope -2/8 or -1/4

so the slope of a perpendicular line is +4

its equation is y = 4x + b, but (5,0) lies on it, so
0 = 4(5) + b
b = -20

new equation: y = 4x - 20

and the y-intercept is -20, (since we have it in slope y-intercept form)