Question

Find the equation for the line that passes through the point (1,-3) and that is parallel to the line with the equation 3/2x-2y=-17/2

Answer 1

The equation for the line that passes through the point (1,-3) and that is parallel to the line with the equation $\frac{3}{2}x - 2y = \frac{-17}{2}$ is:

$y = \frac{3}{4}x - \frac{15}{4}$

Solution:

Given that line that passes through the point (1, -3) and that is parallel to the line with the equation $\frac{3}{2}x - 2y = \frac{-17}{2}$

We have to find equation of line

The slope intercept form is given as:

y = mx + c

Where "m" is the slope of line and "c" is the y-intercept

Let us first find slope of line containing equation $\frac{3}{2}x - 2y = \frac{-17}{2}$

$\frac{3}{2}x - 2y = \frac{-17}{2}$

Rearrange the above equation into slope intercept form

$\frac{3x}{2} + \frac{17}{2} = 2y\\\\y = \frac{3x}{4} + \frac{17}{4}$

On comparing the above equation with slope intercept form y = mx + c,

$m = \frac{3}{4}$

So the slope of line containing equation $\frac{3}{2}x - 2y = \frac{-17}{2}$ is $m = \frac{3}{4}$

We know that slopes of parallel lines are equal

So the slope of line parallel to line having above equation is also $m = \frac{3}{4}$

Now let us find the equation of line having slope m = 3/4 and passes through point (1 , -3)

Substitute $m = \frac{3}{4}$ and (x, y) = (1 , -3) in slope intercept form

y = mx + c

$-3 = \frac{3}{4}(1) + c\\\\c = -3 - \frac{3}{4}\\\\c = \frac{-15}{4}$

Thus the required equation of line is:

substitute $m = \frac{3}{4}$ and $c = \frac{-15}{4}$ in slope intercept form

$y = \frac{3}{4}x + \frac{-15}{4}\\\\y =\frac{3}{4}x - \frac{15}{4}$

Thus the equation of line is found out