Question

ons and graphing
graph a line through (1, 3) and (0, - 2)

Explanation:

Step1: Find the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0, - 2)$ and $(x_2,y_2)=(1,3)$. Then $m=\frac{3-(-2)}{1 - 0}=\frac{3 + 2}{1}=5$.

Step2: Find the y - intercept

The point $(0,-2)$ is the y - intercept $b$ since when $x = 0$, $y=-2$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m = 5$ and $b=-2$, we get $y = 5x-2$.

Step4: Graph the line

1. Plot the y - intercept: Plot the point $(0,-2)$ on the coordinate plane.
2. Use the slope to find another point: The slope $m = 5=\frac{5}{1}$. From the point $(0,-2)$, move 1 unit to the right and 5 units up to get the point $(1,3)$.
3. Draw a straight line through the two points $(0,-2)$ and $(1,3)$.

Answer:

Graph a line passing through the points $(0,-2)$ and $(1,3)$ (by first finding the equation $y = 5x-2$ and using the y - intercept and slope to plot points).