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
`(3)/(2)x - 2y = (-17)/(2)` is:

`y = (3)/(4)x - (15)/(4)`

Solution:

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

`(3)/(2)x - 2y = (-17)/(2)`

Rearrange the above equation into slope intercept form

`(3x)/(2) + (17)/(2) = 2y\\\\y = (3x)/(4) + (17)/(4)`

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

`m = (3)/(4)`

So the slope of line containing equation
`(3)/(2)x - 2y = (-17)/(2)` is
`m = (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 = (3)/(4)`

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

Substitute
`m = (3)/(4)` and (x, y) = (1 , -3) in slope intercept form

y = mx + c

`-3 = (3)/(4)(1) + c\\\\c = -3 - (3)/(4)\\\\c = (-15)/(4)`

Thus the required equation of line is:

substitute
`m = (3)/(4)` and
`c = (-15)/(4)` in slope intercept form

`y = (3)/(4)x + (-15)/(4)\\\\y =(3)/(4)x - (15)/(4)`

Thus the equation of line is found out