Figure 1 (attached in the end) represents the graph of the equation [tex]y+6=45(x+3)[/tex].
Further explanation:
The point slope form of a line passing through the point [tex](x_{1},y_{1})[/tex] is as follows:
[tex]\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}[/tex]
Given:
The given equation is [tex]y+6=45(x+3)[/tex].
Step 1:
First we will convert the equation [tex]y+6=45(x+3)[/tex] in point slope form as follows:
[tex]\fbox{\begin\\\ \begin{aligned}y+6&=45(x+3)\\y-(-6)&=45(x-(-3))\end{aligned}\\\end{minispace}}[/tex]
Step 2:
Now, we will compare the equation [tex]y-(-6)&=45(x-(-3))[/tex] with the equation [tex](y-y_{1})=m(x-x_{1})[/tex].
On comparing both the equations it is concluded that value of slope and the point [tex](x_{1},y_{1})[/tex] is as follows:
[tex]\fbox{\begin\\\ \begin{aligned}(x_{1},y_{1})&=(-3,-6)\\m&=45\end{aligned}\\\end{minispace}}[/tex]
Therefore the first coordinate of the line [tex]y+6=45(x+3)[/tex] is [tex](-3,-6)[/tex].
Here, [tex]45[/tex] is the slope of the line and [tex]129[/tex] is the [tex]y[/tex]- intercept of the line.
Step 3:
Now find the second point that satisfies the given equation [tex]y+6=45(x+3)[/tex].
Substitute [tex]x=0[/tex] in the equation [tex]y+6=45(x+3)[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y+6&=45\times(0+3)\\y+6&=135\\y&=135-6\\y&=129\end{aligned}[/tex]
Therefore, the second coordinate is [tex](0,129)[/tex].
Step 4:
Substitute [tex]y=0[/tex] in the equation [tex]y+6=45(x+3)[/tex] to obtain the value of [tex]x[/tex].
[tex]\begin{aligned}y+6&=45\times(x+3)\\y+6&=45x+135\\45x&=-135+6\\45x&=-129\\x&=-\dfrac{129}{45}\\x&=-2.86\end{aligned}[/tex]
Therefore, the third coordinate is [tex](-2.86,0)[/tex].
Thus, the coordinates for the line [tex]y+6=45(x+3)[/tex] are [tex](-3,-6),(0,129)\ \text{and}\ (-2.86,0)[/tex].
Step 5:
Now plot the points [tex](-3,-6),(0,129)\ \text{and}\ (-2.86,0)[/tex] and join them to obtain the graph of teh equation [tex]y+6=45(x+3)[/tex].
Figure 1 (attached in the end) represents the graph of the equation [tex]y+6=45(x+3)[/tex].
Learn more:
1. A problem on graph https://brainly.com/question/2491745
2. A problem on quadratic function https://brainly.com/question/2334270
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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.
