Hello there. To solve this question, we have to remember how to graph a function.
Given the function:
[tex]y=-2x+5[/tex]To graph it, it is important to remember the following properties:
- It is a linear function, that is a first degree polynomial function, hence its graph is a line.
To graph a line, we need at least two points it passes through.
The easiest points are found setting x = 0 and y = 0, called the y-intercept and x-intercept (or root of the function).
Setting x = 0, we find
[tex]y=-2\cdot0+5=5[/tex]So the point (0, 5) is contained in the line.
Setting y = 0, we solve for x:
[tex]0=-2x+5[/tex]Subtract 5 on both sides of the equation
[tex]-5=-2x[/tex]Divide both sides of the equation by a factor of (-2)
[tex]x=\dfrac{5}{2}[/tex]So the point (5/2, 0) is contained in the line.
Considering we'll use integer values to graph the function, as an easier way to find their coordinates in the plane, consider making y = 3, hence
[tex]\begin{gathered} 3=-2x+5 \\ \\ -2=-2x \\ \\ x=1 \end{gathered}[/tex]Therefore the other point we'll use is (1, 3), also contained in the line.
Now, we have the plane:
This is the graph of this function.
