Question

Need a math person's help ASAP.

Answer 1

Figure 1 (attached in the end) represents the graph of the equation $y+6=45(x+3)$.

Further explanation:

The point slope form of a line passing through the point $(x_{1},y_{1})$ is as follows:

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

Given:

The given equation is $y+6=45(x+3)$.

Step 1:

First we will convert the equation $y+6=45(x+3)$ in point slope form as follows:

$\fbox{\begin\\\ \begin{aligned}y+6&=45(x+3)\\y-(-6)&=45(x-(-3))\end{aligned}\\\end{minispace}}$  

Step 2:

Now, we will compare the equation $y-(-6)&=45(x-(-3))$ with the equation  $(y-y_{1})=m(x-x_{1})$.

On comparing both the equations it is concluded that value of slope and the point $(x_{1},y_{1})$ is as follows:

$\fbox{\begin\\\ \begin{aligned}(x_{1},y_{1})&=(-3,-6)\\m&=45\end{aligned}\\\end{minispace}}$

Therefore the first coordinate of the line $y+6=45(x+3)$ is $(-3,-6)$.

Here, $45$ is the slope of the line and $129$ is the $y$- intercept of the line.

Step 3:

Now find the second point that satisfies the given equation $y+6=45(x+3)$.

Substitute $x=0$ in the equation $y+6=45(x+3)$ to obtain the value of $y$.

$\begin{aligned}y+6&=45\times(0+3)\\y+6&=135\\y&=135-6\\y&=129\end{aligned}$

Therefore, the second coordinate is $(0,129)$.

Step 4:

Substitute $y=0$ in the equation $y+6=45(x+3)$ to obtain the value of $x$.

$\begin{aligned}y+6&=45\times(x+3)\\y+6&=45x+135\\45x&=-135+6\\45x&=-129\\x&=-\dfrac{129}{45}\\x&=-2.86\end{aligned}$  

Therefore, the third coordinate is $(-2.86,0)$.

Thus, the coordinates for the line $y+6=45(x+3)$ are $(-3,-6),(0,129)\ \text{and}\ (-2.86,0)$.

Step 5:  

Now plot the points $(-3,-6),(0,129)\ \text{and}\ (-2.86,0)$ and join them to obtain the graph of teh equation $y+6=45(x+3)$.

Figure 1 (attached in the end) represents the graph of the equation $y+6=45(x+3)$.

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.

Answer 2

we know that

the equation of the line in the point-slope form is equal to

$y-y1=m(x-x1)$

we have

$y+6=45(x+3)$  

so

the point is $(-3,-6)$

the slope is $m=45$

With the slope and the point, find the second point

$m=45=\frac{4.5}{0.10}$

the x-coordinate of the second point will be

$-3+0.10=-2.90$

the y-coordinate of the second point will be

$-6+4.5=-1.5$

the second point is $(-2.90,-1.5)$    

Graph the line

the answer in the attached figure