Question

Which equation represents a line that passes through (-9,-3)

Answer 1

I believe there is something missing in your given, if not then the equation is as follows:
It has the form y=mx+b, where m is the slope, and b is the y-intercept. If this line passes through (-9, -3),its slope is (-3)/(-4) = 3/4

now the equation becomes : y = (3/4).x + b. To calculate b, replace x and y by their respective values in (-9,-3):

-3 = (3/4)(-9) + b ; and b= 15/4, Hence the final equation is :

y= (3/4).x +15/4

Answer 2

The equation of the line is $\boxed{y =  - 6x - 57}$ that passes through the point $\left( { - 9, - 3} \right)$ and has slope of $\boxed{ - 6}.$

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 point is $\left( { - 9, - 3} \right).$

The slope of the line is $– 6.$

Explanation:

The slope of the line is $m =  - 6.$

Substitute $-6$ for $m, -9$ for $x$ and $-3$ for $y$ in equation $y = mx + c$ to obtain the value of c.

$\begin{aligned}- 3&=\left( { - 6}\right)\left( { - 9} \right) + c\\- 3&= 54 + c\\- 3 - 54&=c\\- 57&=c\\\end{aligned}$

Substitute $-57$ for $c$ and $-6$ for m in equation $y = mx + c.$

$\begin{aligned}y&= \left( { - 6} \right)x - 57\\y&=- 6x - 57\\\end{aligned}$

The equation of the line is $\boxed{y =  - 6x - 57}$ that passes through the point $\left( { - 9, - 3} \right)$ and has slope of $\boxed{ - 6}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers, slope -6, passes (-9,-3), slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.