I've tried so hard on this and I'm completely hopeless, can somebody help me out? Please it would mean a lot. Task 1 find the rate of change for each table, equation, or graph. How did you find the rate of change?

Question

Task 1
A.
X 2 4 6
Y 10 20 30
Rate of change:
How did you find the rate of change:

B.
5x +3y= -2
Rate of change:
How did you find the rate of change:

Write an equation in slope-intercept, point-slope or standard form for the line with the given information. Explain why you chose the form you used.
Task 2
A.
Passes through (-1,4), (-5,2)
Equation:
Explain why you chose the form you used:

B.
Slope 2 , y-intercept -4
Equation:
Explain why you chose the form you used:

C.
Has an x-intercept of 6 and a y-intercept of 3
Equation:
Explain why you chose the form you used:

D.
Passes through (1,2) with slope
Equation:
Explain why you chose the form you used:

Please help :(

Answer 1

the rate of change is the slope of the line. That is, if x changes by 1, how much does y change?

In the slope-intercept form, the rate of change (slope) is m, in

y = mx+b

The point-slope form of a line is

y-k = m(x-h)

where the line passes through (h,k) with slope m. It's just another way of writing

(y-k)/(x-h) = m

That is, the slope (m) is the ratio of the change in y over the change in x.

I'm sure all of this is explained in your text, with examples.

So, with all this info, you should have a handle on solving the problems you posted.

If you are given a slope and an intercept, choose the slope-intercept form.

If you are given a point and a slope, use the point-slope form.

If you are given two points, figure the slope, then use one of the points and the point-slope form.