What is the y-intercept of 2x-3y=24

The y-intercept, b, is the value of y when x = 0.

To find the y-intercept, we must first transform the original equation into its slope-intercept form, y = mx + b:

2x - 3y = 24

Subtract 2x on both sides of the equation:

2x - 3y - 2x =  -2x + 24

-3y = -2x + 24

Divide both sides of the equation by -3:

Now that we have the equation in its slope-intercept form, we can find the y-intercept by substituting x with 0:

y = -2/3(0)- 8

y = 0 - 8

y = -8

Therefore, the y-intercept is (0, -8), or b = -8

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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