Question

How do you solve the system by graphing `y = -1/2x + 1` and `y = 1/4x - 2`?

Answer 1

See answer below

Explanation:

Given: `y = -1/2 x + 1 " and " y = 1/4 x - 2`

When the line is in the form `y = mx + b`, `" "b` is the `y`-intercept which is the point `(0, b)`

1. Graphing `y = -1/2 x + 1` by

a. first placing a point at `(0, 1)`.

b. The slope = `m = -1/2` means go down one `y` space and over to the right 2 spaces and place another point. Since
`-1/2 = (-1)/2 = 1/(-2),` you can also go up one `y` and to the left (negative) 2 `x` spaces.

1. Graphing `y = 1/4 x - 2` by

a. first placing a pint at `(0, -2)`.

b. The slope = 1/4 which means go up one `y` space and over to the right 4 `x` spaces and place another point.

The intersection point is the solution to the system of equations.

The solution is `(4, -1)`. This is the point that both lines share.

graph{(y+1/2x - 1)(y-1/4x+2)=0 [-10, 10, -5, 5]}