Question

. Find the equation of a line passing through the point (3, -4) and parallel to the line 3x+2y
-5=0​

Answer 1

Answer:

The equation of required line is 3x - 2y - 17 = 0

Step-by-step explanation:

We need to find the equation of line passing through the point (3, -4) and is parallel to the line 3x + 2y - 5 = 0

When two lines are parallel, then they have equal slope

Now, let us first find the slope of line 3x + 2y - 5 = 0

Reduce the equation of line in slope intercept form, we get

$3x - 2y - 5 = 0\\\\ 2y = 3x - 5\\\\y = \frac{3}{2}x - \frac{5}{2}$

Comparing the equation with y = mx + c, where m= slope

We have

Slope of line, $m = \frac{3}{2}$

Thus, slope line passing through (3, -4) is $\frac{3}{2}$

Now, using the slope intercept form of line, we can get the equation of required line.

Slope intercept for of line is as follows:

$(\,y - y1)\, = m(\,x - x1)\,$

Substituting $m = \frac{3}{2}$, x1 = 3 and y1 = -4, we get

$(\,y - (\,-4)\,)\, = \frac{3}{2} \times (\,x - 3)\,\\\\ y + 4 = \frac{3}{2} \times (\,x - 3)\,\\\\ 2(\,y + 4\,)\, = 3(\,x - 3)\,\\\\ 2y +8 = 3x - 9\\\\3x - 2y - 17 = 0$

Thus, equation of required line is 3x - 2y - 17 = 0