Question

Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below. (0, -2) and -2/3.

Answer 1

y = -(5/2)x -2

Explanation:

The general formula for a straight line is y – mx + b.

The image below shows the graph of the line.

Step 1. Calculate the slope.

Slope = m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

x₁ = 0; y₁ = -2

x₂ = -2; y₂ = 3 Calculate m

m = [3-(-2)]/(-2-0)

m = (3+2)/(-2)

m = 5/(-2)

m = -5/2

Step 2. Calculate the y-intercept

When x = 0, y = 2.

The y-intercept (b) is at y = -2

Step 3. Write the equation for the graph

y = mx + b

y = -(5/2)x - 2

Answer 2

The graph is attached.

Explanation:

We start by plotting the point of the y-intercept. The graph passes through (0, -2); this is on the y-axis, so this is the y-intercept.

From here we use the slope to find the next point. Slope is rise/run. Since our slope is -2/3, this means from our y-intercept, we go down 2 and over to the right 3 and plot our next point. We then draw a line between the two points.