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In the following exercise, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-2,2) and parallel to the line whose equation is 2x-3y=7

Answer :

We know that two lines are parallel if they have the same slope.

Now, recall that the slope of a line in general form:

[tex]Ax+By=C[/tex]

is:

[tex]-\frac{A}{B}.[/tex]

Therefore the slope of the lines represented by the given equation is:

[tex]-\frac{2}{-3}=\frac{2}{3}.[/tex]

Using the slope-point formula for the equation of a line we get that the equation of a line that is parallel to the given line and passes through (-2,2) is:

[tex]y-2=\frac{2}{3}(x-(-2)).[/tex]

Simplifying the above result we get:

[tex]y-2=\frac{2}{3}(x+2).[/tex]

Answer:

[tex]y-2=\frac{2}{3}(x+2)[/tex]

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