Question

Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3) y = -2x + 1/3 y = -2/3x + 1 y = -2x + 1 y = -2/3x + 1/3

Answer 1

`\large\boxed{y=-(2)/(3)x+(1)/(3)}`

Explanation:

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

`y=mx+b`

m - slope

The formula of a slope:

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

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We have the points (2, -1) and (5, -3). Substitute:

`m=(-3-(-1))/(5-2)=(-2)/(3)=-(2)/(3)`

We have the equation:

`y=-(2)/(3)x+b`

Put the coordinates of the point (2, -1):

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

`-1=-(4)/(3)+b` add 4/3 to both sides

`(1)/(3)=b\to b=(1)/(3)`

Finally:

`y=-(2)/(3)x+(1)/(3)`