Answer:
[tex]y = \frac{5}{2}x - 7[/tex]
Step-by-step explanation:
Given the two points, you'll have to solve for the slope. Once you have the slope, then you could easily solve for the y-intercept and have the equation of the line.
First, given the following points, (6, 8) and (2, -2):
Let (x1, y1) = (2, -2)
(x2, y2) = (6, 8)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [8 - (-2)] / (6 - 2)
m = (8 + 2) / 4
m = 10/4
m = 5/2 (This is the slope of the line).
Next, we need to determine the y-intercept. The y-intercept is the y-coordinate of the point (0, b) where the graph crosses the y-axis. Using the slope, m = 5/2, and one of the given points, (6, 8), substitute these values into the slope-intercept form to solve for the y-intercept, b:
y = mx + b
[tex]8 = \frac{5}{2}(6) + b[/tex]
8 = 15 + b
Subtract 15 from both sides to isolate b:
8 - 15 = 15 - 15 + b
-7 = b
Therefore, the y-intercept, b = -7. And its coordinates: (0, -7).
Now that we have our slope, m = 5/2, and y-intercept, b = -7, we can establish the equation of the line in its slope-intercept form:
[tex]y = \frac{5}{2}x - 7[/tex]
To graph the equation, start by plotting the y-intercept, (0, -7), then plot the next points using the slope, 5/2 (rise 5 units, run 2 units).
