Question

Complete the table of values for y = 2x + 6 . Then graph the points to create a line.Use your graph to state:State: x intercept:______ y intercept:_______ slope:_______

Answer 1

Given equation

`y=2x+6\ldots(1)`

put x = 0 in equation (1) we get,

`\begin{gathered} y=2(0)+6 \\ y=0+6 \\ y=6 \end{gathered}`

put x = 1 in equation (1) we get,

`\begin{gathered} y=\text{ 2(1)+6} \\ y=\text{ 2+6} \\ y=8 \end{gathered}`

put x = -2 in equation (1) we get,

`\begin{gathered} y=\text{ 2(-2) +6} \\ y=-4+6 \\ y=2 \end{gathered}`

put x = 2 in the equation (1) we get,

`\begin{gathered} y=\text{ 2(2)+6} \\ y=\text{ 4+6} \\ y=\text{ 10} \end{gathered}`

The table will look like this,

to find the x intercept put y= 0 in the equation (1) and to find y intercept put x = 0 in the quation (1) we get ,

x - intercept = (-3,0)

y - intercept = (0,6)

to find the slope we use the formula,

`m=(y_2-y_1)/(x_2-x_1)`

consider two points , say (0,6) and (1,8)

`\begin{gathered} x_1=0,y_1=6 \\ x_2=1,y_2=8 \end{gathered}`

Now, subsitute the above values in slope formula we get,

`\begin{gathered} m=(8-6)/(1-0) \\ m=2 \end{gathered}`

Thus, slope is 2