Question

Slope of 1/3 and passing through the point (3,2)

Answer 1

To determine the equation of the line that has slope m=1/3 and passes through the point (3,2) you have to use the point-slope form:

`y-y_1=m(x-x_1)`

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line

Replace the formula above with the known information about the line:

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

Next is to write the equation in slope-intercept form, which means that you have to leave the y term alone on the left side of the equation and all other terms have to be on the right side.

-First, distribute the multiplication on the parentheses term:

`\begin{gathered} y-2=(1)/(3)\cdot3-(1)/(3)\cdot3 \\ y-2=(1)/(3)x-1 \end{gathered}`

-Second, pass "-2" to the right side of the equation by applying the opposite operation, "+2", to both sides of the equal sign:

`\begin{gathered} y-2+2=(1)/(3)x-1+2 \\ y=(1)/(3)x+1 \end{gathered}`

So, the equation of the line with slope 1/3 that passes through the point (3,2), expressed in slope-intercept form is:

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