Complete the equation of the line through (3,-1) and (4,7) use exact nhumbers

Answer 1

To find the equation of the line passing through the points (3, -1) and (4, 7), we can use the formula for the slope-intercept form of a line:

y = mx + b

where m is the slope and b is the y-intercept.

First, let's find the slope (m):

m = (y₂ - y₁)/(x₂ - x₁)
m = (7 - (-1))/(4 - 3)
m = (7 + 1)/(4 - 3)
m = 8/1
m = 8

Now that we have the slope (m = 8), we can substitute one of the given points (let's use (3, -1)) into the equation to solve for b.

-1 = 8(3) + b
-1 = 24 + b
b = -1 - 24
b = -25

Now that we have the slope (m = 8) and the y-intercept (b = -25), we can write the equation of the line:

y = 8x - 25