Question

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 1

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

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

`Ax+By=C`

is:

`-(A)/(B).`

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

`-(2)/(-3)=(2)/(3).`

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:

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

Simplifying the above result we get:

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

Answer:

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