Question

my system of equations consists of two lines. one line passes through (2, 3) and (0, 5). the other line passes through (1, 1) and (0, -1). my graph is

Explanation:

Step1: Find first line's equation

First, calculate the slope of the line through (2, 3) and (0, 5):
$m_1 = \frac{5-3}{0-2} = \frac{2}{-2} = -1$
The y-intercept is 5 (from point (0,5)), so the equation is $y = -x + 5$.

Step2: Find second line's equation

Calculate the slope of the line through (1, 1) and (0, -1):
$m_2 = \frac{-1-1}{0-1} = \frac{-2}{-1} = 2$
The y-intercept is -1 (from point (0,-1)), so the equation is $y = 2x - 1$.

Step3: Find intersection point

Set the two equations equal to solve for $x$:
$-x + 5 = 2x - 1$
$5 + 1 = 2x + x$
$6 = 3x$
$x = 2$
Substitute $x=2$ into $y = 2x -1$:
$y = 2(2) -1 = 3$
The intersection point is (2, 3).

Step4: Match to correct graph

The first line $y=-x+5$ has a negative slope and y-intercept 5; the second line $y=2x-1$ has a positive slope and y-intercept -1, intersecting at (2,3). This matches Graph J.

Answer:

Graph J