Find the gradient of the line 2y -8x = -2 Find the y-intercept of the line 3y=-15x -15
Does the point (3,15) lie on the line y=10+2x?
25 points to whoever answers all of them

Step-by-step explanation:

1. In order to find the gradient of equation, you have to make it into slope-form equation y = mx + b :

So m represents gradient. In this question, m is 4.

2. Make it into slope-form equation :

In this question, y-intercept is b which is -5.

3. You have to substitute x-coodinate into the equation to see whether it is equal to y-coordinate :

yes

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt