Question

What is the equation of the line that goes through (-5,0) and (-4,4)

Answer 1

`y=4x+20`

Explanation:

To write an equation, use the slope-intercept equation:

`y=mx+b`

M is the slope and b is the y-intercept.

First, find the slope by using 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. Substitute values:

`(-5,0)(-4,4)\\(-5(x1),0(y1))\\(-4(x2),4(y2))\\\\(4-0)/(-4-(-5))`

Simplify parentheses (two negatives make a positive) and simplify:

`(4-0)/(-4+5)\\\\(4)/(1)=4`

The slope, m, is 4. Insert this information into the equation:

`y=4x+b`

Now, take one of the points and insert into the slope-intercept formula:

`(-5,0)\\(-5(x),0(y))\\\\0=4(-5)+b`

Solve for b, the y-intercept. Simplify multiplication:

`0=-20+b`

Add 20 to both sides and simplify:

`0+20=-20+20+b\\20=b\\b=20`

The y-intercept, b, is 20. Insert this value into the equation:

`y=4x+20`

Done.