Answer:
x-intercept: We know that for the x-intercept, the y-coordinate aka f(x) will always be 0. That's how we know that the x-intercept is 3, since when x = 3, f(x) = 0
rate of change: Finding the equation of the line in slope-intercept form will allow us to find both the rate of change (synonym for slope) and y-intercept. The general equation of slope-intercept form is y = mx + b, where
- (x, y) are any point on the line,
- m is the slope ,
- and b is the y-intercept
Given at least two points on a line, we can find the slope using the slope formula, which is
m = (y2 - y1) / (x2 - x1), where
- m is the slope,
- (x1, y1) are one point on the line,
- and (x2, y2) are another point on the line
Allowing (-1, -8) to be our (x1, y1) point and (3, 0) to be our (x2, y2) point, we can find the slope of the line:
m = (0 - (-8)) / (3 - (-1))
m = (0 + 8) / (3 + 1)
m = 8 / 4
m = 2
y-intercept: Now that we've found the slope, we can plug in any of the coordinates for x and y and 2 for m into the slope-intercept form. This will allow us to solve for b and find our y-intercept. Let's use (-1, -8) for x and y:
y = mx + b
-8 = 2(-1) + b
-8 = -2 + b
-6 = b
Thus, the y-intercept is -6