Respuesta :
The equation for the line that passes through the point (1,-3) and that is parallel to the line with the equation [tex]\frac{3}{2}x - 2y = \frac{-17}{2}[/tex] is:
[tex]y = \frac{3}{4}x - \frac{15}{4}[/tex]
Solution:
Given that line that passes through the point (1, -3) and that is parallel to the line with the equation [tex]\frac{3}{2}x - 2y = \frac{-17}{2}[/tex]
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 [tex]\frac{3}{2}x - 2y = \frac{-17}{2}[/tex]
[tex]\frac{3}{2}x - 2y = \frac{-17}{2}[/tex]
Rearrange the above equation into slope intercept form
[tex]\frac{3x}{2} + \frac{17}{2} = 2y\\\\y = \frac{3x}{4} + \frac{17}{4}[/tex]
On comparing the above equation with slope intercept form y = mx + c,
[tex]m = \frac{3}{4}[/tex]
So the slope of line containing equation [tex]\frac{3}{2}x - 2y = \frac{-17}{2}[/tex] is [tex]m = \frac{3}{4}[/tex]
We know that slopes of parallel lines are equal
So the slope of line parallel to line having above equation is also [tex]m = \frac{3}{4}[/tex]
Now let us find the equation of line having slope m = 3/4 and passes through point (1 , -3)
Substitute [tex]m = \frac{3}{4}[/tex] and (x, y) = (1 , -3) in slope intercept form
y = mx + c
[tex]-3 = \frac{3}{4}(1) + c\\\\c = -3 - \frac{3}{4}\\\\c = \frac{-15}{4}[/tex]
Thus the required equation of line is:
substitute [tex]m = \frac{3}{4}[/tex] and [tex]c = \frac{-15}{4}[/tex] in slope intercept form
[tex]y = \frac{3}{4}x + \frac{-15}{4}\\\\y =\frac{3}{4}x - \frac{15}{4}[/tex]
Thus the equation of line is found out
