Question

Write the equation of the line in slope-intercept form using the two points: E(-1, 3) and F(-2, -3).

Answer 1

`\large\boxed{y=6x+9}`

Explanation:

The slope-intercept form of the equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points E(-1, 3) and F(-2, -3). Substitute:

`m=(-3-3)/(-2-(-1))=(-6)/(-2+1)=(-6)/(-1)=6`

Therefore the equation of a line is:

`y=6x+b`

Put the coordinates of the point E(-1, 3) to the equation and solve it for b:

`3=6(-1)+b`

`3=-6+b` add 6 to both sides

`9=b\to b=9`

Finally we have:

`y=6x+9`