Question

Write the equation of the line that passes through the points (-6, -9) and (7, 7).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answer 1

Answer:

$\displaystyle y + 9 = \frac{16}{13} ( x + 6 )$

Step-by-step explanation:

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

Given a line passes through points A(x1,y1) and B(x2,y2), the slope can be calculated with the equation:

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

We are given the points (-6,-9) and (7,7), thus the slope is:

$\displaystyle m=\frac{7+9}{7+6}=\frac{16}{13}$

Now we apply the point-slope formula using the point (-6,-9):

$\mathbf{\displaystyle y + 9 = \frac{16}{13} ( x + 6 )}$

This equation is expressed in the required format

Answer 2

The equation of the line passing through the given points is required.

The equation of the line is $y=\dfrac{16}{13}x-\dfrac{21}{13}$

The points are $(-6,-9)$ and $(7,7)$

The equation is

$y-y_1=\dfrac{\Delta y}{\Delta x}(x-x_1)\\\Rightarrow y+9=\dfrac{7+9}{7+6}(x+6)\\\Rightarrow y+9=\dfrac{16}{13}x+\dfrac{96}{13}\\\Rightarrow y=\dfrac{16}{13}x-\dfrac{21}{13}$

The equation of the line is $y=\dfrac{16}{13}x-\dfrac{21}{13}$

Learn more:

https://brainly.com/question/1581995?referrer=searchResults