Enter the equation of the line in slope-intercept form

Question

The line perpendicular to y=-2x that passes (0,0)

The equation of the line that passes through (0,0) is y=?

Answer 1

Hello, Jake,

Slope-intercept form is an equation having the following form:

y = mx + b

"m" is the slope, of the rate at which y changes when x is changed. A slope of 2 would mean y would go up by2 each time x is increase by 1. "b" is the y-intercept. It is the value of Y when x=0 (the equation simplifies to y = b, since x = 0).

You have an equation of y = -2x. Boring, but we'll go with what we're given. The equation tells us that the line crosses y at 0, when x is zero. The slope of a negative 2 tells us the line is sloping downwards as we go the the right. Every time I increase x by 1, y decreases by 1. . . [-1],

A line perpendicular to y=-2x has a slope (m) the is the negative inverse of the original slope. Take the slope of 2, invert it (1/2) and apply a negative sign to arrive at -(1/2).

That was easy. The new line head up as x increases. So we know that the new equation will look like this: y = -(1/2)x + b.

We are told that it must go through the point (0,0). To find the y-intercept (b), we simply enter the x and y values and solve for b:

0 = -(1/2)*0 + b

b = 0

Usually this step is slightly more exciting, but it easy to calculate b with a point is given.

The final equation is y = -(1/2)x, or y = 0.5x

The red line is the original equation (positive slope) and the blue line is perpendicular, and goes through (0,0).

Bob