Question

Use the graph to answer the question. 5 3 1 5 4 3 2 1 EN 4 5 2 N -3 -4 TVhich line is perpendicular to the line shown on the graph? O À y=-x+2 Oc y=x+1 OD. y = 2 x + 1 +1 B. y=-37-4

Answer 1

`A)y=-(3)/(2)x+2`

Step-by-step explanation

Step 1

find the slope of the given line

you can find the slope using:

`\begin{gathered} \text{slope}=m=\frac{change\text{ in y }}{\text{change in x}}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}`

P1 and P2 are 2 known points of the line

then,let

P1(0,-1)

P2(3,1)

replace

`\begin{gathered} m_1=\frac{change\text{ in y }}{\text{change in x}}=(y_2-y_1)/(x_2-x_1) \\ m_1=(1-(-1))/(3-0)=(2)/(3) \end{gathered}`

Step 2

Now, 2 lines are perpendicular if the product of their slopes equals - 1

`\begin{gathered} m_1\cdot m_2=-1 \\ \text{Let} \\ m_1=(2)/(3) \\ \text{replace} \\ (2)/(3)\cdot m_2=-1 \\ \text{Multiply both sides by 3/2} \\ (2)/(3)\cdot m_2\cdot(3)/(2)=-1\cdot(3)/(2) \\ m_2=-(3)/(2) \end{gathered}`

Hence, the line we are looking for has a slope of -3/2

`\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \end{gathered}`

the number with the variable is the slope, so find in the optiions the answer with :

`-(3)/(2)x`

so, the answer is

`A)y=-(3)/(2)x+2`