Question

You have two numbers. If you double the first number and add it to the second number, the sum is 10. An equation to represent this situation could be: 2x + y = 10 1) Plot at least five points on this coordinate plane that make the statement and your equation true. What do you notice about the points you have plotted? 2) Using a different color, plot 3 point in the same coordinate plane that do not make the equation true.

Answer 1

(a) See attachment 1

All points lie on the same line

(b) See attachment 2

Explanation:

Given

`2x + y = 10`

Solving (a): Plot 5 points that make the equation, true

First, we calculate the points

Make y the subject

`y = 10 - 2x`

`x = 0 \to y = 10 - 2* 0 = 10`

`x = 1 \to y = 10 - 2* 1 = 8`

`x = 2 \to y = 10 - 2* 2 = 6`

`x = 3 \to y = 10 - 2* 3 = 4`

`x = 4 \to y = 10 - 2* 4 = 2`

So, we will plot the following points

`(0,10)\ (1,8)\ (2,6)\ (3,4)\ (4,2)`

See attachment 1

Notice that all points lie on the same line

Solving (b):

Point (5,7) does not make the equation true, and that is why it lies outside the line

See attachment 2