Answer:
[tex]y = \frac{4}{3} x + 17[/tex]
Step-by-step 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, [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:
[tex]\frac{(17)-(13)}{(0)-(-3)} \\= \frac{17-13}{0+3} \\= \frac{4}{3}[/tex]
Thus, the slope is [tex]\frac{4}{3}[/tex].
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 [tex]y = mx + b[/tex] format. Substitute the [tex]m[/tex] and [tex]b[/tex] for real values.
The [tex]m[/tex] represents the slope of the equation, so substitute it for [tex]\frac{4}{3}[/tex]. The [tex]b[/tex] represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:
[tex]y = \frac{4}{3} x + 17[/tex]
