Question

Write the equation of the line that passes through the given points.
(0, -1) and ( - 13, -4)

Answer 1

Linear Equations

We typically write linear equations in slope-intercept form:

`y=mx+b`

• m = slope
• b = y-intercept (the value of y when x=0)

Solving the Question

We're given:

• Line passes through (0, -1) and ( -13, -4)

1) Determine the slope (m)

To find the slope, we can use the slope equation:

`m=(y_2-y_1)/(x_2-x_1)` where
`(x_1,y_1)` and
`(x_2,y_2)` are two points through which the line passes

⇒ Plug in the given points:

`m=(-1-(-4))/(0-(-13))\\\\m=(-1+4)/(0+13)\\\\m=(3)/(13)`

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

`y=(3)/(13)x+b`

1) Determine the y-intercept (b)

In this case, the y-intercept is already given to us.

The y-intercept is the value of y when x=0. Given that the line passes through (0,-1), we know that this is -1.

Plug this into
`y=(3)/(13)x+b`:

`y=(3)/(13)x+(-1)\\\\y=(3)/(13)x-1`

Answer

`y=(3)/(13)x-1`