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

Jul 7, 2018

#### Explanation:

Given: $y = - \frac{1}{2} x + 1 \text{ and } y = \frac{1}{4} x - 2$

When the line is in the form $y = m x + b$, $\text{ } b$ is the $y$-intercept which is the point $\left(0 , b\right)$

1. Graphing $y = - \frac{1}{2} x + 1$ by

a. first placing a point at $\left(0 , 1\right)$.

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

1. Graphing $y = \frac{1}{4} x - 2$ by

a. first placing a pint at $\left(0 , - 2\right)$.

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 $\left(4 , - 1\right)$. This is the point that both lines share.

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