Question

Find an equation for the line below

Answer 1

`y=\displaystyle -(1)/(4)x+\displaystyle (15)/(4)`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept.

1) Determine the slope (m)

`m=\displaystyle (y_2-y_1)/(x_2-x_1)` where two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

In the graph, two points are indicated: (-5,5) and (3,3). Plug these into the equation:

`m=\displaystyle (3-5)/(3-(-5))\\\\m=\displaystyle (3-5)/(3+5)\\\\m=\displaystyle (-2)/(8)\\\\m=\displaystyle (-1)/(4)`

Therefore, the slope of the line is
`\displaystyle -(1)/(4)`. Plug this into
`y=mx+b`:

`y=\displaystyle -(1)/(4)x+b`

2) Determine the y-intercept (b)

`y=\displaystyle -(1)/(4)x+b`

Plug in one of the points we used earlier and solve for b:

`3=\displaystyle -(1)/(4)(3)+b\\\\3=\displaystyle -(3)/(4)+b\\\\3+\displaystyle (3)/(4)=b\\\\(15)/(4) =b`

Therefore,
`\displaystyle (15)/(4)` is the y-intercept. Plug this back into
`y=\displaystyle -(1)/(4)x+b`:

`y=\displaystyle -(1)/(4)x+\displaystyle (15)/(4)`

I hope this helps!