Write an equation of a line that passes through the points (5, 7) and (2, 16)

y = -3x + 22

Step-by-step explanation:

In this question, we have to make an equation with the given information.

First, we need to find the slope using the slope equation: m = y2-y1/x2-x1

Solve for the slope by plugging in coordinates:

m = 16 - 7/2 - 5

m = 9/-3

m = -3

Now, we know that the slope of the line is -3.

We have to find the y-intercept of the equation, to do this, we would plug in some of our given information to the y = mx + b equation.

We would use our slope (-3) and one of the coordinates to solve for b.

Solve:

7 = -3(5) + b

7 = -15 + b

Add 15 to both sides.

22 = b

We now know that our y-intercept is 22. Now we can gather all of our new information to make our equation:

y = -3x + 22

The equation of the line is y = -3x + 22

step-by-step explanation: