Question

*PLEASE HELP WILL GIVE 60 POINTS I'M DESPERATE*

This table models a linear function.
X: -8 -4 4 8
Y: -3 0 6 9
Enter the COORDINATES of the y-intercept in the boxes.
(_,_)

Answer 1

(0, 3)

Explanation:

1. Find the slope:

`(y_(2) -y_(1) )/(x_(2)-x_(1) ) =(0-(-3))/(-4-(-8))\\ \\=(3)/(4)`

2. Calculate the y-intercept using a given point:

(-8, -3)

-3 =
`(3)/(4) (-8)` + b

-3 = -6 + b

-3+6 = -6+6 + b

3 = b

3. Write in slope intercept form:

`y= (3)/(4) x+3`

Therefore, the y-intercept is 3.

The graph for this table is shown below.

hope this helps :)

Answer 2

y-intercept = (0, 3)

Explanation:

This table models a linear function:

`\begin{tabular}\cline{1-2} $x$ & $y$\\\cline{1-2} -8 & -3\\\cline{1-2} -4 & 0\\\cline{1-2} 4 & 6\\\cline{1-2} 8 & 9\\\cline{1-2} \end{tabular}`

Find the slope:

`\sf slope\:(m)=(change\:in\:y)/(change\:in\:x)=(9-6)/(8-4)=(3)/(4)`

Use one of the points (-4, 0) and the found slope to form a linear equation using the point-slope formula:

`\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-0 & =(3)/(4)(x-(-4)\\\\y & =(3)/(4)x+3\end{aligned}`

The y-intercept is when x = 0:

`\implies y=(3)/(4)(0)+3=3`

Therefore, the y-intercept is (0, 3)