The equation for the line that passes through the point (1,-3) and that is parallel to the line with the equation
is:
![y = \frac{3}{4}x - \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%7D%7B4%7Dx%20-%20%5Cfrac%7B15%7D%7B4%7D)
<h3><u>
Solution:</u></h3>
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}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7Dx%20-%202y%20%3D%20%5Cfrac%7B-17%7D%7B2%7D)
We have to find equation of line
<em><u>The slope intercept form is given as:</u></em>
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}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7Dx%20-%202y%20%3D%20%5Cfrac%7B-17%7D%7B2%7D)
![\frac{3}{2}x - 2y = \frac{-17}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7Dx%20-%202y%20%3D%20%5Cfrac%7B-17%7D%7B2%7D)
Rearrange the above equation into slope intercept form
![\frac{3x}{2} + \frac{17}{2} = 2y\\\\y = \frac{3x}{4} + \frac{17}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B2%7D%20%2B%20%5Cfrac%7B17%7D%7B2%7D%20%3D%202y%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B3x%7D%7B4%7D%20%2B%20%5Cfrac%7B17%7D%7B4%7D)
On comparing the above equation with slope intercept form y = mx + c,
![m = \frac{3}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
So the slope of line containing equation
is ![m = \frac{3}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
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}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
<em><u>Now let us find the equation of line having slope m = 3/4 and passes through point (1 , -3)</u></em>
Substitute
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}](https://tex.z-dn.net/?f=-3%20%3D%20%5Cfrac%7B3%7D%7B4%7D%281%29%20%2B%20c%5C%5C%5C%5Cc%20%3D%20-3%20-%20%5Cfrac%7B3%7D%7B4%7D%5C%5C%5C%5Cc%20%3D%20%5Cfrac%7B-15%7D%7B4%7D)
<em><u>Thus the required equation of line is:</u></em>
substitute
and
in slope intercept form
![y = \frac{3}{4}x + \frac{-15}{4}\\\\y =\frac{3}{4}x - \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%7D%7B4%7Dx%20%2B%20%5Cfrac%7B-15%7D%7B4%7D%5C%5C%5C%5Cy%20%3D%5Cfrac%7B3%7D%7B4%7Dx%20-%20%5Cfrac%7B15%7D%7B4%7D)
Thus the equation of line is found out