Question

What is the y-intercept of the line perpendicular to the line y = -x + 3 that includes the point (3, 1)?

Answer 1

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 a line to be perpendicular to another line, the slope has to be the negative reciprocal of the original line's slope.

For example:

Slope(m) = $\frac{1}{2}$

Perpendicular line's slope: $-\frac{2}{1}$   or -2         [positive to negative]

m = $-\frac{3}{1}$  or  -3

Perpendicular line's slope: $\frac{1}{3}$        [negative to positive]

y = -x + 3

m = -1         So the perpendicular line's slope is 1, now plug it into the equation

y = mx + b

y = x + b     To find b, plug in the point (3, 1) into the equation

1 = 3 + b     Subtract 3 on both sides to get b by itself

1 - 3 = 3 - 3 + b

-2 = b      The y-intercept is -2