Question

Which equation represents a line that passes through (–9, –3) and has a slope of –6?
1. y – 9 = –6(x – 3)
2. y + 9 = –6(x + 3)
3. y – 3 = –6(x – 9)
4. y + 3 = –6(x + 9)

Answer 1

y - y1 = (x - x1)
slope(m) = -6
(-9,-3)....x1 = -9 and y1 = -3
now we sub
y - (-3) = -6(x - (-9) =
y + 3 = -6(x + 9)

Answer 2

The equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $\fbox{\begin\\\ \math y+3=-6(x+9)\\\end{minispce}}$ i.e., $\fbox{\begin\\\bf{option 4}\\\end{minispce}}$.

Further explanation:

It is given that the line passes through the point $(-9,-3)$ and the slope of the line is $-6$.

Since, the slope of the line and one point through which the line passes is known so use the point slope form of the line to obtain the equation of the line.

The point slope form of a line is given as follows:

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

In equation $(1)$ the term $m$ is called the slope and $(x_{1},y_{1})$ is the point through which the line passes.

Consider the point $(-9,-3)$ as $(x_{1},y_{1})$ and the slope of the line is $-6$ so, the value of $m$ is $-6$.

To obtain the equation of the line, substitute $-6$ for $m$, $-9$ for $x_{1}$ and $-3$ for $y_{1}$ in equation $(1)$.

$\fbox{\begin\\\ \math (y+3)=(-6)(x+9)\\\end{minispace}}$

Therefore, the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $\fbox{\begin\\\ \math y+3=-6(x+9)\\\end{minispace}}$.

Option 1:

In the option 1 it is given that the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y-9=-6(x-3)$.

But as per our calculation made above the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y+3=-6(x+9)$.

This implies that option 1 is incorrect.

Option 2:

In the option 2 it is given that the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y+9=-6(x+3)$.

But as per our calculation made above the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y+3=-6(x+9)$.

This implies that option 2 is incorrect.

Option 3:

In the option 3 it is given that the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y-3=-6(x-9)$.

But as per our calculation made above the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y+3=-6(x+9)$.

This implies that option 3 is incorrect.

Option 4:

In the option 4 it is given that the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y+3=-6(x+9)$.

As per our the calculation the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $y+3=-6(x+9)$.

This implies that option 4 is correct.

Therefore, the correct option is option 4.

Thus, the equation of the line which passes through the point $(-9,-3)$ and with slope of $-6$ is $\fbox{\begin\\\ \math y+3=-6(x+9)\\\end{minispace}}$ i.e., option 4.

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: Coordinate geometry

Keywords: Geometry, coordinate geometry, slope, intercept, equation, point slope form, slope intercept form, lines, (-9,-3), y+3=-6(x+9), intercept form, slope of -6, x-intercept, y-intercept.