Question

identify the slope and y-intercept of the line below.
show your work here
slope =
y-intercept

Explanation:

Step1: Identify two points

From the graph, we can see two clear points: \((0, 2)\) (the y - intercept point) and \((4, - 1)\) (another point on the line). Also, we can use \((-4,5)\) and \((0,2)\) or \((0,2)\) and \((4, - 1)\). Let's use \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(4, - 1)\)

Step2: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substitute \(x_1 = 0,y_1=2,x_2 = 4,y_2=-1\) into the formula:
\(m=\frac{-1 - 2}{4-0}=\frac{-3}{4}=-\frac{3}{4}\)

Step3: Identify the y - intercept

The y - intercept is the point where the line crosses the y - axis. At this point, \(x = 0\). From the graph, when \(x = 0\), \(y=2\). So the y - intercept \(b = 2\)

Answer:

Slope: \(-\frac{3}{4}\), y - intercept: \(2\)