Write the equation of the line that is perpendicular to y=5x+7 and passes through the point (10,3)

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be negative reciprocals of each other. (flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or  

Perpendicular line's slope =  (flip the sign from + to -, and flip the fraction)

Slope =

Perpendicular line's slope =  (flip the sign from - to +, and flip the fraction)

y = 5x + 7      The slope is 5, so the perpendicular line's slope is

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

   To find b, plug in the point (10, 3) into the equation, then isolate/get the variable "b" by itself

3 = -2 + b    Add 2 on both sides to get "b" by itself

3 + 2 = -2 + 2 + b

5 = b

x=30

step-by-step explanation: