Question

What is an equation of the line that passing through the points (-2, -5) and (4, 7) ?

Answer 1

`y=2x-1`

Explanation:

Use the slope-intercept formula:
`y=mx+b` where m is slope and b the y-intercept.

`(-2,-5)(4,7)`

Use the slope formula for when you have two points:

`(y(2)-y(1))/(x(2)-x(1))=(rise)/(run)`

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

`(7-(-5))/(4-(-2))`

Simplify parentheses (negative+negative=positive)

`(7+5)/(4+2)`

Simplify

`(12)/(6)=2`

2 is the slope:

`y=2x+b`

Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:

(4,7)

`y=2x+b\\7=2(4)+b`

`7=8+b\\7-8=8-8+b\\7-8=b\\-1=b\\b=-1`

The y-intercept is -1. Insert into the equation. Change the + symbol to -:

`y=2x-1`

Done.