Question

plot the points (0,0), (3,2), and (6,4) on graph paper. then draw a line through the points. name the coordinates of three more points on the same line.

Explanation:

Step1: Find the slope of the line

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,0)$ and $(3,2)$, we have $m=\frac{2 - 0}{3 - 0}=\frac{2}{3}$.

Step2: Find the equation of the line

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through $(0,0)$, $b = 0$. So the equation of the line is $y=\frac{2}{3}x$.

Step3: Find three more points

Let $x = 9$, then $y=\frac{2}{3}\times9 = 6$, so the point is $(9,6)$.
Let $x=12$, then $y=\frac{2}{3}\times12 = 8$, so the point is $(12,8)$.
Let $x = 15$, then $y=\frac{2}{3}\times15=10$, so the point is $(15,10)$.

Answer:

$(9,6),(12,8),(15,10)$