Question

I have a question for a graph

Answer 1

Hello there. To solve this question, we have to remember how to graph a function.

Given the function:

$y=-2x+5$

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

$y=-2\cdot0+5=5$

So the point (0, 5) is contained in the line.

Setting y = 0, we solve for x:

$0=-2x+5$

Subtract 5 on both sides of the equation

$-5=-2x$

Divide both sides of the equation by a factor of (-2)

$x=\dfrac{5}{2}$

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

$\begin{gathered} 3=-2x+5 \\ \\ -2=-2x \\ \\ x=1 \end{gathered}$

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.