Question

Suppose the line through points (x,6) and (1,2) is parallel to the graph of 2x + y =3. Find the value of x.

Answer 1

Step 1:

In this question, we are given that:

Suppose the line through points (x,6) and (1,2) is parallel to the graph of 2x + y =3. Find the value of x.

Step 2:

Given the two points, (x,6) and (1,2), we need to find the slope.

`\begin{gathered} slope,\text{ m =}(y_2-y_1)/(x_2-x_1) \\ (x_1,y_1)\text{ = ( x , 6 )} \\ (x_2,y_2)\text{ = ( 1, 2)} \end{gathered}`
`m\text{ = }(2-6)/(1-x)=(-4)/(1-x)`

Next, we find the slope of 2x+y = 3 ( Given y = mx + c )

( General Equation of a line)

`\begin{gathered} y\text{ = -2x + 3} \\ \text{comparing with y = mx + c , we have that:} \\ \text{m = -2} \end{gathered}`

Step 3:

Now, the two lines are parallel, which means that:

`\begin{gathered} m_1=m_2 \\ (-4)/(1-x)=\text{ -2} \end{gathered}`

So, we need to find x .

`\begin{gathered} We\text{ cross-multiply, and we have that:} \\ -4\text{ = -2 ( 1-x)} \\ -4=-2+2x \\ -4\text{ + 2= 2x} \\ -2\text{ = 2x} \\ \text{Divide both sides by 2, we have that:} \\ \text{x =}(-2)/(2) \\ x\text{ = -1} \end{gathered}`

Check:

Recall that the two points are: (x,6) and (1,2)

Now, x = -1

which means: ( -1, 6) and ( 1, 2)