Question

Use the given conditions to write an equation for the line in point-slope form and general form.Passing through (-2,3) and parallel to the line whose equation is 7x-2y-5=0

Answer 1

We know that two lines are parallel if and only if their slopes are equal. For this reason, we need to find the slope of line given by the equation 7x-2y-5=0 in order to get the slope of the equation we are looking for; to do this we solve the equation for y:

$\begin{gathered} 7x-2y-5=0 \\ 2y=7x-5 \\ y=\frac{7}{2}x-\frac{5}{2} \end{gathered}$

Now, this equation is written in slope-intercept form:

$y=mx+b$

Comparing it with the equation we found we conclude that the slope is 7/2 and hence the equation we are looking for will also have this slope.

Now that we know this, we have to remember that the equation of a line that passes through the point (x1,y1) and has slope m is given by:

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

Plugging the slope we found and the point given we have:

$\begin{gathered} y-3=\frac{7}{2}(x+2) \\ y-3=\frac{7}{2}x+7 \\ y=\frac{7}{2}x+10 \end{gathered}$

Therefore, the equation of the line we are looking for in slope intercept form is:

$y=\frac{7}{2}x+10$

To write in general form we write it in the form Ax+By+C=0:

$\begin{gathered} y=\frac{7}{2}x+10 \\ 2y=7x+20 \\ 7x-2y+20=0 \end{gathered}$

Therefore, the equation of the line in general form is:

$7x-2y+20=0$