Question

richard cuts a peice of wood for a project the first cut is shown and can be represented by the equation y=1/2x+2 the second cut need to be parellel to the first it will pass through the point (0,-7) identify the equation that represents richards second cut

Answer 1

B)

Explanation:

First, lets try to build the second equation, it has the general shape

`y=m *x+b`

Where b is a constant (a number) and m the slope, another constant.

Using the given condition (0,-7) you can find the first constant of our second equation, just put "0" where you see "x", and put -7 where there is a "y".

That gives us that b is equals to -7.

Now we only need to know that the condition for 2 linear equations to be parallels is that their slope have to be the same or multiple between each others, this means that "m" of our second equation has to be equal to 1/2

thus, our second equation is
`y=(1)/(2)*x-7`

Another way to see this is that you can compare two linear equations y1=m1*x1 + b1, and y2=m2*x2+b2, if these two intersect in somewhere, this condition should meet:

X= (b1-b2)/(m2-m1).

If the slopes are the same, the above equation gives us an error, meaning that the linear equations are, in fact parallels.