Question

which function has the greatest y- intercept? A. f(x)= 3x) B. 2x+3y=12 ) C. the line that has a slope of 2 and passes through (-1,-4) D. a graph ​

Answer 1

`\boxed{\text{(4) The graph}}`

Explanation:

The question is asking, which function has the greatest value when x = 0?

We must evaluate f(0) for each one.

(1) ƒ(x) = 3x

f(0) = 3 × 0 = 0

(2) 2x + 3y = 12

Let x = 0.

2 × 0 + 3y = 12

0 + 3y = 12

3y = 12

y = 4

(3) The line

The line has a slope of 2, and y= -4 when x = 1.

y increases by 2 when x increases by 1.

For the same reason, y decreases by 2 when x decreases by 1.

Thus, when x decreases from 1 to 0, y decreases from -4 to -6.

f(0) = -6.

(4) The graph

The graph has a y-intercept at y = 5, so,

f(0) = 5.

`\boxed{\textbf{The graph}}` has the greatest y-intercept.

Answer 2

#4

Explanation:

1) The y intercept is 0.

2) Convert to slope-intercept form:

2x + 3y = 12

3y = -2x + 12

y = -2/3 x + 4

So the y-intercept is 4.

3) Write in point-slope form:

y + 4 = 2 (x - 1)

Now convert to slope-intercept form:

y + 4 = 2x - 2

y = 2x - 6

So the y-intercept is -6.

4) The y-intercept is 5.

So of the four lines, #4 has the largest y-intercept.