Final answer:
The equation of the line passing through the points (9,3) and (0,-4) in slope-intercept form (y = mx + b) is y = -7/9x + 10.
Step-by-step explanation:
The equation of the line passing through the points (9,3) and (0,-4) in slope-intercept form (y = mx + b) can be found using the formula:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the coordinates of the two points into the formula:
m = (-4 - 3) / (0 - 9) = -7/9
Next, substitute one of the points and the slope into the formula to calculate the y-intercept (b):
y = mx + b
3 = (-7/9)(9) + b
b = 3 + 7
b = 10
Therefore, the equation of the line in slope-intercept form is y = -7/9x + 10.