Question

Write equation for (-6,5) and (-3,-3)

Answer 1

Answer:

$y=-\frac{8}{3}x-11$

Step-by-step explanation:

Given:

Two points on a line are given as:

(-6, 5) and (-3, -3)

Now, equation of a line with two points $(x_1,y_1)\ and\ (x_2,y_2)$ is given as:

$y-y_1=m(x-x_1)$

Where, 'm' is the slope and is given as:

$m=\frac{y_2-y_1}{x_2-x_1}$

Now, plugging the value of 'm' in the above equation, we get:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Here, $(x_1,y_1)=(-6,5)\ and\ (x_2,y_2)=(-3,-3)$

$y-5=(\frac{-3-5}{-3-(-6)})(x-(-6))\\\\y-5=(\frac{-8}{-3+6})(x+6)\\\\y-5=\frac{-8}{3}(x+6)\\\\y-5=-\frac{8}{3}x-16\\\\y=-\frac{8}{3}x-16+5\\\\y=-\frac{8}{3}x-11$

Therefore, the equation of a line passing through (-6,5) and (-3,-3) is:

$y=-\frac{8}{3}x-11$