To find the equation of the line that passes through the points (4, -8) and (7, -6), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the line. The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (4, -8) and (7, -6):
m = (-6 - (-8)) / (7 - 4)
= 2 / 3
Now that we have the slope, we can substitute it into the slope-intercept form equation:
y = (2/3) * x + b
To find the y-intercept (b), we can substitute the coordinates of one of the given points into the equation. Let's use the point (4, -8):
-8 = (2/3) * 4 + b
-8 = 8/3 + b
To solve for b, we subtract 8/3 from both sides:
-24/3 - 8/3 = b
-32/3 = b
So the equation of the line in slope-intercept form is:
y = (2/3) * x - (32/3)