Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

`y=-6x+2`

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

`m=\displaystyle (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)`

Given the graph, we determine which points we could use. For example, we could use the two points
`(0,2)` and
`(1,-4)`:

`m=\displaystyle (-4-2)/(1-0)\\\\m=\displaystyle (-6)/(1)\\\\m=-6`

Therefore, the slope of the line is -6. Plug this into
`y=mx+b`:

`y=-6x+b`

2) Determine the y-intercept (b)

Recall that the y-intercept occurs when x=0. Given the point (0,2), we know that the y-intercept is 2. Plug this into
`y=-6x+b`:

`y=-6x+2`

I hope this helps!