Question

Based on the graph, what are the rate of change and the y intercept of the line.

Answer 1

Answer:

The rate of change is 1/2 and the y-intercept is 1

Step-by-step explanation:

You can calulate the rate of change by picking two points on the graph and using the slope formula

(y2-y1)/(x2-x1)

so in this example you can use the points (2,2) represeting (x1,y1) and (4,3) representing (x2,y2)

When you plug into the slope formula you get:

(3-2)/(4-2) = 1/2 which is the slope.

The y-intercept is where the line intersects the y=axis and can be  seen as the coordinate pair (0, #) where the # is the y intercept. From the graph you can see the y-intercept is 1, but you can aslo solve for the y-intercept using the slope-intercept equation:

y=mx+b

where b is the y-intercept and m is the slope.

so using a slope of 1/2 and a coordinate of (2,2) you get:

y-2=(1/2)(x-2)

y = (1/2x)-1+2

y = (1/2x) + 1

so now the equation is in slope-intecept form and you can see the slope is 1/2 and the y-intercept is 1