Question

1A) Sketch the graph y=3x-6 and identify the vertical interceptB) Sketch the graph Y= -0.6x+2 and identify the vertical interceptC) Sketch the graph Y=1/4x - 5/4 and identify the vertical intercept

Answer 1

We must graph and find the intercepts with the y-axis of the following equations:

A) Y = 3X - 6

B) Y = -0.6X + 2

C) Y = 1/4X - 5/4

All equations above are of the form Y = mx + b

where, b is the vertical intercept or the intercept with the y-axis

Now, let's start with equation A

A) Y = 3X - 6

to graph we need to locate two points

the two easiest points are when X = 0 and the other is when Y = 0

let's make x=0

`\begin{gathered} Y=3\cdot0-6 \\ Y=-6 \end{gathered}`

so our first point in the graph is (0,-6)

now, when Y=0

`\begin{gathered} 0=3x-6 \\ 6=3x \\ (6)/(3)=x \\ x=2 \end{gathered}`

so, our second point is (2,0)

now that we know that the equation Y = 3X - 6 passes through the points (0, -6) and (2,0), we only have to join them with a straight line

B) Y = -0.6X + 2

when x=0, then y = 2

therefore point 1 is (0,2), which corresponds to the vertical intercept

for our second point: when y=0, then...

`\begin{gathered} 0=-0.6x+2 \\ -2=-0.6x \\ (-2)/(-0.6)=x \\ x=3.33 \end{gathered}`

therefore our second point is (3.33 , 0) or as a fraction (10/3 , 0)

this is how the graph will look like