Figure 1 (attached in the end) represents the graph of the equation
.
Further explanation:
The point slope form of a line passing through the point
is as follows:
![\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%5C%5C%5C%20%5Cmath%20%28y-y_%7B1%7D%29%3Dm%28x-x_%7B1%7D%29%5C%5C%5Cend%7Bminispace%7D%7D)
Given:
The given equation is
.
Step 1:
First we will convert the equation
in point slope form as follows:
Step 2:
Now, we will compare the equation
with the equation
.
On comparing both the equations it is concluded that value of slope and the point
is as follows:
![\fbox{\begin\\\ \begin{aligned}(x_{1},y_{1})&=(-3,-6)\\m&=45\end{aligned}\\\end{minispace}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%5C%5C%5C%20%5Cbegin%7Baligned%7D%28x_%7B1%7D%2Cy_%7B1%7D%29%26%3D%28-3%2C-6%29%5C%5Cm%26%3D45%5Cend%7Baligned%7D%5C%5C%5Cend%7Bminispace%7D%7D)
Therefore the first coordinate of the line
is
.
Here,
is the slope of the line and
is the
- intercept of the line.
Step 3:
Now find the second point that satisfies the given equation
.
Substitute
in the equation
to obtain the value of
.
![\begin{aligned}y+6&=45\times(0+3)\\y+6&=135\\y&=135-6\\y&=129\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dy%2B6%26%3D45%5Ctimes%280%2B3%29%5C%5Cy%2B6%26%3D135%5C%5Cy%26%3D135-6%5C%5Cy%26%3D129%5Cend%7Baligned%7D)
Therefore, the second coordinate is
.
Step 4:
Substitute
in the equation
to obtain the value of
.
Therefore, the third coordinate is
.
Thus, the coordinates for the line
are
.
Step 5:
Now plot the points
and join them to obtain the graph of teh equation
.
Figure 1 (attached in the end) represents the graph of the equation
.
Learn more:
1. A problem on graph brainly.com/question/2491745
2. A problem on quadratic function brainly.com/question/2334270
3. A problem on graph of a function brainly.com/question/9590016
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equation
Keywords: Linear equations, linear form, equation, line, slope, intercept, coordinate, solutions set, graph, curve, degree, polynomial, quadratic equation.