The equation of the line which passes through the point
and with slope of
is
i.e.,
.
Further explanation:
It is given that the line passes through the point
and the slope of the line is
.
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:
(1)
In equation
the term
is called the slope and
is the point through which the line passes.
Consider the point
as
and the slope of the line is
so, the value of
is
.
To obtain the equation of the line, substitute
for
,
for
and
for
in equation
.
![\fbox{\begin\\\ \math (y+3)=(-6)(x+9)\\\end{minispace}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%5C%5C%5C%20%5Cmath%20%28y%2B3%29%3D%28-6%29%28x%2B9%29%5C%5C%5Cend%7Bminispace%7D%7D)
Therefore, the equation of the line which passes through the point
and with slope of
is
.
Option 1:
In the option 1 it is given that the equation of the line which passes through the point
and with slope of
is
.
But as per our calculation made above the equation of the line which passes through the point
and with slope of
is
.
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
and with slope of
is
.
But as per our calculation made above the equation of the line which passes through the point
and with slope of
is
.
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
and with slope of
is
.
But as per our calculation made above the equation of the line which passes through the point
and with slope of
is
.
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
and with slope of
is
.
As per our the calculation the equation of the line which passes through the point
and with slope of
is
.
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
and with slope of
is
i.e., option 4.
Learn more:
1. A problem to complete the square of quadratic function brainly.com/question/12992613
2. A problem to determine the slope intercept form of a line brainly.com/question/1473992
3. Inverse function 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.