Question

Find the equation of a line passing through the point(3,-4) and having slope -5/7

Answer 1

Given,

A point (3,-4) and the slope of the line is -5/7.

To Find,

The equation of the line.

Solution,

The formula for calculating the equation of the  line when a point and the slope of the line are given is

(y-y₁) = m(x-x₁) where m is the slope of the line and x₁,y₁ is the point lying on the line.

(y+4) = -5/7(x-3)

7y+28 = -5x+15

5x+7y+13 = 0

Hence, the equation of the line is 5x+7y+13 = 0.

Answer 2

Given: A point $(3,-4)$ and having slope $\frac{-5}{7}$

According to the question

A general equation for line having slipe m is $y=mx+c,$ where m is slope of line.

Here $m=\frac{-5}{7}$

So, $7y=-5x+c$

Now to eliminate (we will use the information that line passes through $(3,-4)$.

$-28=-15+c$

which gives $c=-13$

So, equation of line is,

$7y+5x-13=0$