Question

Sketch a graph of the line that runs parallel to the line y = 1/2X-3 and passes through the point (-4,0) below Remember to scale and label your axes!

Answer 1

We need to obtain the formula of the line

General formula of the line

`y=mx+b`

where m is the slope and b the y-intercept

First, if the line is parallel to

`y=(1)/(2)x-3`

has the same slope(1/2)

then we have the slope of the new line, we can replace on the general formula

`y=(1)/(2)x+b`

to find b or y-intercept we can replace the point of the statement on this way we obtain b and we make sure that the new graph passes through this point

then

`(0)=(1)/(2)(-4)+b`

and solve to b

`\begin{gathered} 0=-(4)/(2)+b \\ b=(4)/(2) \\ \\ b=2 \end{gathered}`

now we replace the slope and b on the formula

Graph

`y=(1)/(2)x+2`

now we need to points to graph, we have (-4,0) and the point of the y-intetrcept(the value of b is where x=0)

point of y intercept is (0,2)

we place the two points on the graph and join