Question

identify the equation that describes the line in slope-intercept form. slope =−1/3, point (−2,3) is on the line

Answer 1

`y=(-1)/(3)x+(7)/(3)`

Explanation:

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So here, we're already given your slope which is wonderful! That is less work to figure out. Now we have to put all of this together into slope-intercept form. To recall, the slope-intercept form is:

`y=mx+b`

We have our m, which is our slope
`(-1)/(3)` and we have a point that's on the line (-2, 3). We can actually figure out the equation with all of this information!

All we need to do is to sub in the slope as m and then substitute the point that we have into x and y respectively, so it becomes:

`3=(-1)/(3)(-2)+b`

Now, all we have to do is solve for b:

`3=(1)/(3)*2+b` - Cancelling out the negatives.

`3=(1)/(3)*(2)/(1)+b` - Making the 2 into a fraction for easy multiplication.

`3=(2)/(3) +b`

`3-(2)/(3) =b` - Moving all the values to the other side to solve for b.

`(3)/(1) -(2)/(3)=b` - Making the 3 into a fraction for easy subtraction.

`(9)/(3) -(2)/(3)=b` - Multiplied the first fraction by 3 to get least common denom

`(7)/(3)=b`

Therefore, the formula that can be made from this is:

`y=(-1)/(3)x+(7)/(3)`