Question

Select all the points that are on the graph of the line 2x+4y=20

Answer 1

Answer:

$(x,y)\\\\\Bigg(x, \displaystyle\frac{-1}{2}x+5\Bigg)$

The points on the equation 2x+4y=20.

Step-by-step explanation:

We are given the following in the question:

$2x+4y=20$

Writing this equation in the point slope form,

$y = mx + c$

where m is the slope and c is the y-intercept.

$2x+4y=20\\4y = 20-2x\\\\y =\displaystyle\frac{-1}{2}x+5$

where the slope is $\frac{-1}{2}$ and y-intercept is 5.

The attached image shows graph for the given equation.

All the points on the line for the given equation is of the form:

$(x,y)\\\\\Bigg(x, \displaystyle\frac{-1}{2}x+5\Bigg)$

Answer 2

Answer:

The point (10-2y, y) for any real number y, represents any point on the given line.

Step-by-step explanation:

2x + 4y = 20

Divide both sides by 2.

x + 2y = 10

x = 10 - 2y

So, (10-2y, y) gives us all points on the graph of the line 2x + 4y = 20.

Some sample points:

Let y = 0. Then, 10-2(0) = 10.

Therefore, (10, 0) is one point on the given line.

For y = 1, y = 2 and y = 3,

(8, 1), (6, 2) and (4, 3) are some more points on the line.