Question

Learning Task 1: Graph each pair of linear equations in one coordinate plane.

1. y = 2x + 2 and 2y = 4x + 4
2. Y= x-5 and y = -x + 3
3. Y = 2x-3 and y = 2x + 4​

Answer 1

We kindly invite you to see the explanation and images attached below.

Explanation:

From Geometry we know that every line can be formed by knowing two two distinct points in a plane. Our stategy consist in using two distinct points for each linear equation in order to create our plot.

1)
`y = 2\cdot x + 2`,
`A(x,y) = (0, 2)` and
`B(x,y) = (1,4)`.

The line
`2\cdot y = 4\cdot x + 4` is a multiple of
`y = 2\cdot x + 2`. We present the graph below.

2)
`y = x-5`,
`A(x,y) = (0,-5)` and
`B(x,y) =(1,-4)`.

`y = -x+3`,
`C(x,y) = (0, 3)` and
`D(x,y) = (1,2)`.

Finally, we proceed to plot each line and present the results below.

3)
`y = 2\cdot x-3`,
`A(x,y) = (0,-3)` and
`B(x,y) = (1, -1)`.

`y = 2\cdot x + 4`,
`C(x,y) = (0,4)` and
`D(x,y) = (1,6)`.

Finally, we proceed to plot each line and present the results below.