Question

Hi, I wanted to know if I was doing this right I know how to find the y-intercept but not the x.

Answer 1

So we have the following linear function:

`f(x)=-0.25x+4`

And we must graph the line that it defines. For this purpose we are going to find the x and y intercept first. Remember that in order to graph a line you just need two of its points.

So firstly let's find the y-intercept. The expression for this point is (x,f(x))=(0,f(0)) so we just need to find f(0):

`\begin{gathered} f(0)=-0.25\cdot0+4=0+4 \\ f(0)=4 \end{gathered}`

Which means that the y-intercept is at point (0,4).

The x-intercept is the point where the line meets with the x-axis. At this point the value of y is 0 and since the y-coordinates of the points in the line are given by (x,y)=(x,f(x)) then we can conclude that at the y-intercept f(x)=0. If we solve this equation for x we find the x-intercept:

`f(x)=-0.25x+4=0`

We substract 4 at both sides of the equation:

`\begin{gathered} -0.25x+4=0 \\ -0.25x+4-4=0-4 \\ -0.25x=-4 \end{gathered}`

And we divide both sides by -0.25:

`\begin{gathered} -0.25x=-4 \\ -(0.25x)/(-0.25)=-(4)/(-0.25) \\ x=16 \end{gathered}`

So now we know that the x-intercept is at (16,0).

With these two points already calculated you just need to draw them in the grid. The graph of the function is the line that passes through both. You should end up with something like this:

Remember that the points in the line are given by (x,f(x)). This means that by choosing a random x value and calculating f(x) you can find another point of the line. For example if we take x=4:

`f(4)=-0.25\cdot4+4=-1+4=3`

Which means that point (4,3) is part of the line. Then we can sketch the graph with this point and the y-intercept: