Question

Which equation represents the line that passes through the points (–3, 7) and (9, –1)?

Answer 1

First find the slope of the line.

m=slope=(y2-y1)/(x2-x1), in this case:

m=(-1-7)/(9--3)

m=-8/12

m=-2/3

You did not specify which form of the line you wanted.

Slope-intercept form is y=mx+b

y=-2x/3+b, using pint (9,-1) we can solve for b, the y-intercept...

-1=-2(9)/3+b

-1=-6+b

5=b  then we have:

y=-2x/3+5 or more neatly

y=(-2x+15)/3

Point-slope form of a line is:

y-y1=m(x-x1), again using (9,-1) as the point and m=-2/3 you get:

y+1=(-2/3)(x-9)

Standard form of a line is ax+by+c:

We can rearrange y=(-2x+15)/3 to standard form

y=(-2x+15)/3  multiply both sides by 3

3y=-2x+15  add 2x to both sides

2x+3y=15

Answer 2

The equation of the line that passes through the points $\left({ - 3,7}\right)$ and $\left({9, - 1}\right)$ is $\boxed{2x + 3y = 15}$ .

Further explanation:

The linear equation with slope m and intercept c is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ can be expressed as,

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

Given:

The passes through the points are $\left({ - 3,7}\right)$ and $\left({9, - 1}\right)$ .

Explanation:

The line passes the points that are $\left({ - 3,7}\right)$ and $\left({9, - 1}\right)$.

The slope of the line can be obtained as follows.

$\begin{aligned}m&=\frac{{ - 1 - 7}}{{9-\left({ - 3}\right)}}\\&=\frac{{ - 8}}{{12}}\\&=-\frac{2}{3}\\\end{aligned}$

The slope of the line is m =  $- \frac{2}{3}$.

The line passes through the point $\left({9, - 1}\right)$.

Substitute 9 for x, $- \frac{2}{3}$ for m and -1 for y in equation y = mx + c to obtain the value of c.

$\begin{aligned}-1&=\frac{{-2}}{3}\left(9\right)+c\\-1&=-2\left(3\right)+c\\-1&=-6+c\\-1+6&=c\\5&=c\\\end{aligned}$

Hence, the equation of the line that passes through the points $\left({ - 3,7}\right)$ and $\left({9, - 1}\right)$ is $\boxed{2x + 3y = 15}$.

Learn more:

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2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.