Question

Use the given conditions to write an equation for the line in point slope form and slope intercept form. Passing through (-2,1) and parallel to the line whose equation is x-3y=5

Answer 1

so the answer is y-1=5/3

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Answer 2

The given point is (-2,1) and the given line is x-3y=5.

The slope of the given line can be determined as,

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

The equation of the line which is parallel to the given line will have the same slope.

Thus, the equation of the new line passing through (-2,1) can be determined as,

`\begin{gathered} (y-1)/(x-(-2))=(1)/(3) \\ 3(y-1)=x+2 \\ 3y-3=x+2 \\ 3y=x+5 \\ y=(x)/(3)+(5)/(3) \end{gathered}`

Thus, the equation of the line in slope intercept form is y=x/3+5/3.

The equation of the line in the point slope form can be determined as,

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

Thus, the equation of the line in the point slope form is (y-1)=(x+2)/3