What is the slope of the line that passes through the points left bracket, 7, comma, minus, 5, right bracket(7,−5) and left bracket, 16, comma, 7, right bracket(16,7)? Write your answer in simplest form.
To find the slope of the line that passes through two points, you can use the slope formula:
slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Given the points (7, -5) and (16, 7), we can label these points as follows:
x1 = 7, y1 = -5
x2 = 16, y2 = 7
Now we can plug these into the formula:
m = (7 - (-5)) / (16 - 7)
m = (7 + 5) / (9)
m = 12 / 9
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 3:
m = (12 / 3) / (9 / 3)
m = 4 / 3
So the slope of the line in simplest form is 4/3.