Question

Find an equation for the line that passes through the points (-1,-4) and (5,-2)

Answer 1

Linear Equations

Linear equations are typically organized in slope-intercept form:

`y=mx+b`

• m = the slope of the line
• b = the y-intercept (the value of y when the line crosses the y-axis)

To determine a linear equation in slope-intercept form:

1. Find the slope
2. Plug the slope into y=mx+b
3. Find the y-intercept
4. Plug the y-intercept into y=mx+b

Solving the Question

We're given:

• The line passes through the points (-1,-4) and (5,-2)

First, find the slope of the line (m):

`m=(y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

⇒ Plug in the given points (-1,-4) and (5,-2):

`m=(-2-(-4))/(5-(-1))\\\\m=(-2+4)/(5+1)\\\\m=(2)/(6)\\\\m=(1)/(3)`

⇒ Therefore, the slope of the line is
`(1)/(3)`. Plug this into y=mx+b:

`y=(1)/(3)x+b`

Now, determine the y-intercept (b):

`y=(1)/(3)x+b`

⇒ Plug in one of the points and solve for b:

`-4=(1)/(3)(-1)+b\\\\-4=-(1)/(3)+b\\\\-4+(1)/(3)=b\\\\b=-(11)/(3)`

⇒ Therefore, the y-intercept is
`-(11)/(3)`. Plug this back into our original equation:

`y=(1)/(3)x-(11)/(3)`

Answer

`y=(1)/(3)x-(11)/(3)`