Question

what are the slope and y-intercept of the linear function graphed to the left?
slope: -2; y-intercept: 2
slope: $-\frac{1}{2}$; y-intercept: 1
slope: $\frac{1}{2}$; y-intercept: 2
slope: 2; y-intercept: 1

Explanation:

Step1: Find y - intercept

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at (0, 1), so the y - intercept is 1.

Step2: Calculate the slope

We can use two points on the line. We know the y - intercept is (0, 1) and we can see another point (2, 0) on the line. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(2,0)$. Then $m=\frac{0 - 1}{2 - 0}=\frac{-1}{2}=-\frac{1}{2}$.

Answer:

slope: $-\frac{1}{2}$; y - intercept: 1 (corresponding to the option: slope: $-\frac{1}{2}$; y - intercept: 1)