Question

Find the equation of this line. y= [?]x+[?]

Answer 1

`y=3x-4`

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)`

On the graph, two points are highlighted for us: (0,-4) and (2,2). Plug these into the formula:

`m=\displaystyle(2-(-4))/(2-0)\\\\m=\displaystyle(2+4)/(2)\\\\m=\displaystyle(6)/(2)\\\\m=3`

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

`y=3x+b`

2) Determine the y-intercept (b)

`y=3x+b`

Recall that the y-intercept occurs when x=0. Given the point (0,-4), the y-intercept is therefore -4. Plug this into
`y=3x+b`:

`y=3x+(-4)\\y=3x-4`

I hope this helps!