Question

What is the equation of this graphed line?
please answer in slope-intercept form

Answer 1

`y = (-1)/(3) x - 5`

Explanation:

slope-intercept form y =mx+ b where m is slope and b is y--intercept

slope formula =
`(y2-y1)/(x2-x1)`

point is given as (x,y)

first point (-6,-3) second point (6,-7)

slope m =
`(-7-(-3)))/(6-(-6))) = (-7+3)/(6+6) = (-4)/(12) =(-1)/(3)`

next is to calculate y--intercept

plug in any given point and calculated slope into formula y = mx + b

-3 = (-1/3) * (-6) +b

-3= 2 + b subtract 2 from each side

b = -5

finally equation is
`y = (-1)/(3) x -5`

Answer 2

`y=-(1)/(3)x -5`

Explanation:

Slope-intercept form is
`y=mx+b`, so that's the equation you'll be plugging your values into.

To find the slope of a line, you only need two points, which this graph gives you. (-6, -3) and (6, -7)

Slope, or m, can be found by using
`(y_2-y_1)/(x_2-x_1)`. Now you just plug in your points into the formula, giving you
`((-7)-(-3))/((6)-(-6)) =(-4)/(12) =(-1)/(3)` .

Since you don't have an intercept, choose one of the two given points to plug into the equation
`y-y_1=m(x-x_1)` .

* It doesn't matter which point you use, both will give you a correct answer.

Let's use (-6, -3).

Since you now have a
`y_1, x_1,` and your
`m`, all you need to do is plug them in.

`y-y_1=m(x-x_1)\\y-(-3)=-(1)/(3)(x-(-6))\\y+3=-(1)/(3) (x+6)\\y+3=-(1)/(3) x-2\\y=-(1)/(3) x-5`

If you want, you can plug in points just to confirm that this is the right equation. The simplest way to find out is by making x=0, which gives you a y value of -5. You can see on the graph that the line passes through -5 on the y-axis when x=0, so the equation is valid.