Answer:
The equation in Slope-intercept form:
[tex]y = \frac{2}{3}x + 2[/tex]
Step-by-step explanation:
-Find the slope first, by using the slope formula:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
(where [tex](x_{1},y_{1})[/tex] is the first point and [tex](x_{2},y_{2})[/tex] is the second point).
-Use two given points from the following problem for the slope formula:
[tex]m = \frac{6-2}{6-0}[/tex]
-Then, solve the equation:
[tex]m = \frac{6-2}{6-0}[/tex]
[tex]m = \frac{2}{3}[/tex]
After you have the found the slope, use both the slope [tex]\frac{2}{3}[/tex] and the first point [tex](0,2)[/tex] for the Point-slope formula:
[tex]y - y_{1} = m (x-x_{1})[/tex]
(where [tex]m[/tex] is the slope and [tex](x_{1}, y_{1})[/tex] is the first point).
-The equation in Point-slope form:
[tex]y - 2 = \frac{2}{3} (x-0)[/tex]
Then, you solve:
[tex]y - 2 = \frac{2}{3} (x-0)[/tex]
[tex]y - 2 + 2= \frac{2}{3} (x-0) + 2[/tex]
[tex]y = \frac{2}{3}x + 2[/tex]
-So, the equation in Slope-intercept form would be:
[tex]y = \frac{2}{3}x + 2[/tex]
