Question

Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –x + 9 y = –x + 5 y = –3x – 11y y = –3x + 25

Answer 1

Step $1$

Find the slope of the line

we know that

the formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

Let

$A(-6,7)\\B(-3,6)$

substitute the values

$m=\frac{(6-7)}{(-3+6)}$

$m=\frac{(-1)}{(3)}$

$m=-1/3$

Step $2$

with the slope m and the point $A(-6,7)$ find the equation of the line

we know that

the equation of the line in the point-slope form is equal to

$y-y1=m*(x-x1)$

substitute the values

$y-7=(-1/3)*(x+6)$

$y=(-1/3)x-2+7$

$y=(-1/3)x+5$

therefore

the answer is

$y=(-1/3)x+5$

Answer 2

The equation of the line which passes through the points $(-6,7)$ and $(-3,6)$ is $\fbox{\begin\\\ \math x+3y=15\\\end{minispace}}$.

Further explanation:

It is given that the line passes through the points $(-6,7)$ and $(-3,6)$.

Consider the point $(-6,7)$ as $(x_{1},y_{1})$ and $(-3,6)$ as $(x_{2},y_{2})$.

Two points are given through which the line passes so, in order to determine the equation of the line use the two point form equation.

The general representation of the two point form of a equation is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=\left(\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)(x-x_{1})\\\end{minispace}}$                             (1)

In the above equation the expression $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ is called slope.

Slope of a line is represented as $m$ and the expression for $m$ is as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$       (2)

Substitute $m$ for $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ in equation (1).

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$   (3)

To calculate the value of slope substitute the value of $x_{1},x_{2},y_{1}$ and $y_{2}$ in equation (2).

$\begin{aligned}m&=\frac{6-7}{-3+6}\\&=\dfrac{-1}{3}\end{aligned}$

Therefore, the value of slope of the line is $\frac{-1}{3}$.

To obtain the equation of the line substitute the value of $m, x_{1}$ and $y_{1}$ in equation (3).

$\begin{aligned}(y-7)&=\frac{-1}{3}(x+6)\\3y-21&=-x-6\\x+3y&=15\end{aligned}$

Therefore, the equation of the line is $x+3y=15$.

Thus, the equation of the line which passes through the points $(-6,7)$ and $(-3,6)$ is $\fbox{\begin\\\ \math x+3y=15\\\end{minispace}}$.

Learn more:

1. A problem to complete the square of quadratic function https://brainly.com/question/12992613  

2. A problem to determine the slope intercept form of a line https://brainly.com/question/1473992

3. Inverse function https://brainly.com/question/1632445.

Answer details

Grade: High school

Subject: Mathematics

Chapter: Lines

Keywords: Equation, linear equation, slope, intercept, intersect, graph, curve, slope intercept form, line, point slope form, two point form, equation of a line, (-6,7) and (-3,6).