Answer:
[tex]y = \frac{1}{3}x + \frac{2}{3}[/tex]
Step-by-step explanation:
To find the slope, you can use the slope formula:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
Where (x1, y1) is one set of coordinates with (x2, y2) being the second set.
Step 1 - Plug known values in:
[tex]\frac{2 - 0}{4 -(-2)}[/tex]
[tex]\\\frac{2}{4 + 2}[/tex]
[tex]\\\frac{2}{6}[/tex]
This simplifies to:
[tex]\\\frac{1}{3}[/tex]
The equation y = mx + b states that the m variable is the slope with the b value being the y-intercept, so:
[tex]y = \frac{1}{3}x + b[/tex]
Step 2 - Plug the variables of the second equation in to calculate y intercept:
[tex](4, 2)\\\\2 = \frac{1}{3}(4) + b\\2 = \frac{4}{3} + b[/tex]
Subtract [tex]\frac{4}{3}[/tex] from 2:
[tex]2 - \frac{4}{3} = b\\\frac{6}{3} - \frac{4}{3} = b\\b = \frac{2}{3}[/tex]
Meaning the end equation is:
[tex]y = \frac{1}{3}x + \frac{2}{3}[/tex]
Hope this helps!
