Question

what is the slope and the y - intercept of the line on the graph below?
o slope = - 4, y - intercept = 1
o slope = - 4, y - intercept = 4
o slope = -\frac{1}{4}, y - intercept = 1

Explanation:

Step1: Recall slope - intercept formula

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept

The line crosses the y - axis at the point $(0,1)$, so the y - intercept $b = 1$.

Step3: Calculate the slope

Use two points on the line, say $(0,1)$ and $(4,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 1,x_2 = 4,y_2 = 0$. Then $m=\frac{0 - 1}{4 - 0}=-\frac{1}{4}$.

Answer:

slope = $-\frac{1}{4}$, y - intercept = 1