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Question: How do you graph \(y=-2x+10\) ?...

How do you graph y=−2x+10y=-2x+10 ?

Explanation

Solution

In this question, we have to draw the graph of a given equation. The equation given to us consists of two variables, will we draw a two-dimensional graph. For drawing the graph, we have to use the substitution method to get the values of x and y, so that we can plot a graph. First, we put different values of x in the equation and solve for y. Similarly, we put different values of y in the equation and solve for x. Then, we plot those coordinates in the two-dimensional graph and join all the points to get a required curve or a straight line.

Complete step by step answer:
According to the question, it is given that equation is y=−2x+10y=-2x+10 --------- (1)
We will apply the substitution method in the above equation, that is
Let x=0 in equation (1), we get
⇒y=−2(0)+10 ⇒y=0+10 \begin{aligned} & \Rightarrow y=-2(0)+10 \\\ & \Rightarrow y=0+10 \\\ \end{aligned}
Therefore, we get
⇒y=10\Rightarrow y=10
Thus, coordinate will become A(x,y)=A(0,10)
Let y=0 in equation (1), we get
⇒0=−2x+10\Rightarrow 0=-2x+10
Now, subtract 10 on both sides of the above equation, we get
⇒0−10=−2x+10−10\Rightarrow 0-10=-2x+10-10
As we know, the same terms with different signs cancel out each other, we get
⇒−10=−2x\Rightarrow -10=-2x
Now, divide 2 on both sides of the equation, we get
⇒−102=−22x ⇒−5=−x \begin{aligned} & \Rightarrow \dfrac{-10}{2}=\dfrac{-2}{2}x \\\ & \Rightarrow -5=-x \\\ \end{aligned}
Now, we will multiply (-1) on both sides in the above equation, we get
⇒5=x\Rightarrow 5=x
Thus, coordinate is B(x,y)=B(5,0)
Let x=1 in equation (1), we get
⇒y=−2(1)+10 ⇒y=−2+10 \begin{aligned} & \Rightarrow y=-2(1)+10 \\\ & \Rightarrow y=-2+10 \\\ \end{aligned}
Therefore, we get
⇒y=8\Rightarrow y=8
Thus, coordinate is C(x,y)=C(1,8)
Let y=1 in equation (1), we get
⇒1=−2x+10\Rightarrow 1=-2x+10
Now, subtract 10 on both sides in the above equation, we get
⇒1−10=−2x+10−10\Rightarrow 1-10=-2x+10-10
As we know, the same terms with different signs cancel out each other, we get
⇒−9=−2x\Rightarrow -9=-2x
Now, divide 2 on both sides of the above equation, we get
⇒−92=−22x ⇒−4.5=−x \begin{aligned} & \Rightarrow \dfrac{-9}{2}=\dfrac{-2}{2}x \\\ & \Rightarrow -4.5=-x \\\ \end{aligned}
Now, multiply (-1) on both sides of the equation, we get
⇒−4.5.(−1)=−x.(−1)\Rightarrow -4.5.(-1)=-x.(-1)
Therefore we get
⇒4.5=x\Rightarrow 4.5=x
Thus, coordinate is D(x,y)=D(4.5,1)
After finding these coordinates A(0,10), B(5,0), C(1,8), and D(4.5,1), we will plot these points on the graph, that is

After plotting these points, join these points to get a curve of equation y=−2x+10y=-2x+10 .


Therefore, for the equation y=−2x+10y=-2x+10 , we have plotted the graph using different coordinates.

Note: Do all the calculations carefully to avoid calculation mistakes. For plotting the graph, atleast find 4 coordinates to get a perfect curve or a straight line. Always mention the points on the graph.