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
