Hello!
To find the equation of the line that passes through the points (0, -8) and (4, -3), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
First, we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0, -8) and (x2, y2) = (4, -3). Substituting these values, we get:
m = (-3 - (-8)) / (4 - 0) = 5/4
So the slope of the line is 5/4. Now we can use the point-slope form of the equation with either of the given points. Let's use the point (0, -8):
y - (-8) = 5/4(x - 0)
Simplifying this equation, we get:
y + 8 = 5/4x
Subtracting 8 from both sides, we get the final equation:
y = 5/4x - 8
So the equation of the line that passes through the points (0, -8) and (4, -3) is y = 5/4x - 8.