graph the line that represents each linear equation.\n1. $y = x + 3$\n2. $y=-5x + 1$\n3. $y=\frac{2}{3}x - 5$

Explanation:

Step1: Find the y - intercept

For a linear equation in the form $y = mx + b$, $b$ is the y - intercept.

1. For $y=x + 3$, when $x = 0$, $y=3$. For $y=-5x + 1$, when $x = 0$, $y = 1$. For $y=\frac{2}{3}x-5$, when $x = 0$, $y=-5$.

Step2: Find the x - intercept

Set $y = 0$ and solve for $x$.

1. For $y=x + 3$, $0=x + 3$, so $x=-3$. For $y=-5x + 1$, $0=-5x + 1$, then $5x=1$ and $x=\frac{1}{5}$. For $y=\frac{2}{3}x-5$, $0=\frac{2}{3}x-5$, $\frac{2}{3}x=5$, $x=\frac{15}{2}=7.5$.

Step3: Plot the points and draw the line

1. For $y=x + 3$, plot the points $(0,3)$ and $(-3,0)$ and draw a straight line through them.
2. For $y=-5x + 1$, plot the points $(0,1)$ and $(\frac{1}{5},0)$ and draw a straight line through them.
3. For $y=\frac{2}{3}x-5$, plot the points $(0,-5)$ and $(7.5,0)$ and draw a straight line through them.

Answer:

Graphs are drawn by first finding the y - intercepts $(0,3)$, $(0,1)$, $(0,-5)$ and x - intercepts $(-3,0)$, $(\frac{1}{5},0)$, $(7.5,0)$ respectively for the equations $y=x + 3$, $y=-5x + 1$, $y=\frac{2}{3}x-5$ and then drawing straight lines through the pairs of points.