Question

a system of equations is graphed here. which system of equations does the graph represent? a $y = 3x + 2$ $y = -2x + 5$ b $y = 3x - 2$ $y = 2x + 5$ c $y = -3x + 2$ $y = 2x - 5$ d $y = -3x - 2$ $y = -2x - 5$

Explanation:

Step1: Analyze the first line (positive slope)

We can use two points on the line with positive slope, e.g., \((-2, -4)\) and \((1, 5)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - (-4)}{1 - (-2)}=\frac{9}{3}=3\). Using point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(1,5)\), we get \(y - 5 = 3(x - 1)\), which simplifies to \(y=3x+2\).

Step2: Analyze the second line (negative slope)

We use two points on the line with negative slope, e.g., \((-2,9)\) and \((3, - 1)\). The slope \(m\) is \(m=\frac{-1 - 9}{3-(-2)}=\frac{-10}{5}=-2\). Using point - slope form with \((x_1,y_1)=(1,5)\) (the intersection point), \(y - 5=-2(x - 1)\), which simplifies to \(y=-2x + 5\).

Answer:

A. \(y = 3x+2\)
\(y=-2x + 5\)