Question

a graph shows a line passing through the points (0, 2) and (3, 5). questions: 1. find the slope of the line. 2. identify the y - intercept. 3. write the equation of the line in slope - intercept form. y = 1x+2

Explanation:

Step1: Calculate the slope

The slope - formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(3,5)$, then $m=\frac{5 - 2}{3 - 0}=\frac{3}{3}=1$.

Step2: Identify the y - intercept

The y - intercept is the y - coordinate of the point where the line crosses the y - axis. The point $(0,2)$ is on the y - axis, so the y - intercept $b = 2$.

Step3: Write the slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substituting $m = 1$ and $b = 2$ into the formula, we get $y=1x+2$ or simply $y=x + 2$.

Answer:

1. The slope of the line is $1$.
2. The y - intercept is $2$.
3. The equation of the line in slope - intercept form is $y=x + 2$.