Question

Examine the linear table to find the slope, y-intercept, and write the equation for this linear relationship ​. NEED HELP PLEASE

Answer 1

`y = (4)/(3) x + 17`

Explanation:

The table shows a set of x and y values, thus showing a set of points we can use to find the equation.

1) First, find the slope by using two points and substituting their x and y values into the slope formula,
`(y_2-y_1)/(x_2-x_1)`. I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:

`((17)-(13))/((0)-(-3)) \\= (17-13)/(0+3) \\= (4)/(3)`

Thus, the slope is
`(4)/(3)`.

2) Next, identify the y-intercept. The y-intercept is where the line hits the y-axis. All points on the y-axis have a x value of 0. Thus, (0,17) must be the y-intercept of the line.

3) Finally, write an equation in slope-intercept form, or
`y = mx + b` format. Substitute the
`m` and
`b` for real values.

The
`m` represents the slope of the equation, so substitute it for
`(4)/(3)`. The
`b` represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:

`y = (4)/(3) x + 17`