Final answer:
To write the equation of a line given two points, first calculate the slope (m) using the rise over run, and then find the y-intercept (b) using the slope and one of the points. The final equation is y = -3x + 8.
Step-by-step explanation:
Given two points, (3,-1) and (-2,14), we can find the slope ('m') by calculating the rise over run.
To find the y-intercept ('b'), we can plug the value of the slope and one of the points into the equation and solve for 'b'.
Step 1: Calculate the slope (m)
m = (y2 - y1) / (x2 - x1)
= (14 - (-1)) / (-2 - 3)
= 15 / (-5)
= -3
Step 2: Find the y-intercept (b)
Using the point (3, -1) and the slope -3:
-1 = (-3)(3) + b
-1 = -9 + b
b = -1 + 9
b = 8
Therefore, the equation of the line in y=mx+b form is y = -3x + 8.