Question

find the slope and the y-intercept of the graph of the linear equation. then sketch the equation, if the line is slope-intercept form.
the slope is \\(\square\\) (simplify your answer.)

Explanation:

Step1: Identify two points on line

From the graph, we can take the y-intercept $(0, -2)$ and another point $(4, 1)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{1 - (-2)}{4 - 0}=\frac{3}{4}$

Step3: Identify y-intercept

The line crosses the y-axis at $(0, -2)$, so $b=-2$.

Step4: Write slope-intercept equation

Use form $y=mx+b$
$y=\frac{3}{4}x - 2$

Answer:

The slope is $\frac{3}{4}$
The slope-intercept equation is $y=\frac{3}{4}x - 2$