Respuesta :

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.

Ver imagen AmalyaJ50215
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