Question

The function h(x) shown in the table below is a linear function. Identify its slope and y-intercept, and write its formula in slope-intercept form.

Answer 1

To find the slope of the table, we need to use the next formula:

`m=(y_2-y_1)/(x_2-x_1)`

Replace taking two points from the given table.

Then, P1(0,-3) and P2(1,-7):

`m=(-7-(-3))/(1-0)=(-4)/(1)=-4`

Now, we can use the next equation to get the slope- intercept form:

`y-y_1=m(x-x_1)`

Relace using P(0,-3) and m-4.

Therefore:

`\begin{gathered} y-(-3)=-4(x-0) \\ y+3=-4 \\ Solve\text{ for y to get the equation line:} \\ y=-4x-3 \end{gathered}`

Finally, we get the slope-intercept form y=mx+b.

Where b represents the y-intercept.

The y-intercept is -3.

In conclusion:

Slope = -4

y-intercept b= -3

Formula h(x) = -4x-3