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Sagot :
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:
[tex]y-y_1=m(x-x_1)[/tex]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:
[tex]y-2=\frac{1}{3}(x-3)[/tex]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:
[tex]\begin{gathered} y-2=\frac{1}{3}\cdot3-\frac{1}{3}\cdot3 \\ y-2=\frac{1}{3}x-1 \end{gathered}[/tex]-Second, pass "-2" to the right side of the equation by applying the opposite operation, "+2", to both sides of the equal sign:
[tex]\begin{gathered} y-2+2=\frac{1}{3}x-1+2 \\ y=\frac{1}{3}x+1 \end{gathered}[/tex]So, the equation of the line with slope 1/3 that passes through the point (3,2), expressed in slope-intercept form is:
[tex]y=\frac{1}{3}x+1[/tex]
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