Which equation represents the line that passes through
the points (2, -1) and (6, 7)?
A y=x-2
y = 2x - 4
C y = 2x - 3
y = 2x - 5
B
D

y = 2x - 5

Step-by-step explanation:

The equation that represents the line that passes through the points (2, -1) and (6, 7) can be gotten by

Step 1

Finding the slope of the line

m = (y2 - y1) / (x2 - x1)

Points on lines are represented as coordinates (x, y)

We are given two points

Point 1 has coordinates (2, -1) which corresponds to (x2, y2)

Point 2 has coordinates (6, 7) which corresponds to (x1, y1)

Therefore,

x2= 2

y2 = -1

x1 = -6

y1 = 7

The slope,

m = (-1 - 7) / (2 - 6)

m = -8 / -4

m = 2

Step 2

The slope of a line can be gotten between any two points on the line and it is equal at any two points on the same line.

Let us assume a third point on the line has coordinates (x, y)

And given one point on the line with coordinates (6, 7)

Since, the slope of a line can be gotten between any two points and is equal, then we can say

m = (-1 - 7) / (2 - 6) = (y - 7) / (x - 6)

m = 2 = (y - 7) / (x - 6)

2 = (y - 7) / (x - 6)

Step 3

2 = (y - 7) / (x - 6)

Cross multiply

y - 7 = 2(x - 6)

y - 7 = 2x - 12

Step 4

Make y subject of formula by adding 7 to both sides of the equation

y - 7 + 7 = 2x - 12 + 7

y = 2x - 5

Step 5

y = 2x - 5 is the slope-intercept form equation of the line.

all it means is function 3