To find the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22), we first need to calculate the slope of the line. The slope (m) can be found using the formula:
m = (y₂ – y₁) / (x₂ – x₁)
Here, we can set (x₁, y₁) to be (5, 7) and (x₂, y₂) to be (8, 22). Plugging in these values, we get:
m = (22 – 7) / (8 – 5) = 15 / 3 = 5
Now that we have the slope, we can use one of the points to find the y-intercept (b). We’ll use the point (5, 7). The slope-intercept form of a line is given by:
y = mx + b
Substituting in the slope we found:
7 = 5(5) + b
Simplifying this equation:
7 = 25 + b
Now, we solve for b:
b = 7 – 25 = -18
Now we have both the slope and the y-intercept. The slope-intercept form of the line is:
y = 5x – 18
This is the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22).