Answer:
y = 2x - 5
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.