Question

Find at least ten solutions to the linear equation 1/2x + y = 5, and plot the points on a coordinate plane. What shape is the graph of the linear equation taking?

Answer 1

The linear equation 1/2x + y = 5, we can choose values for x and solve for y. When we plot the points on a coordinate plane, we get a line graph.

Step-by-step explanation:

To find solutions to the linear equation 1/2x + y = 5, we can arbitrarily choose values for x and solve for y.

Let's choose x = 0:
1/2(0) + y = 5
y = 5
So one solution is (0, 5).

Now let's choose x = 2:
1/2(2) + y = 5
1 + y = 5
y = 4
Another solution is (2, 4).

We can continue this process and find more solutions:
x = 4, y = 3
x = 6, y = 2
x = 8, y = 1
x = 10, y = 0
x = -2, y = 6
x = -4, y = 7
x = -6, y = 8
x = -8, y = 9
x = -10, y = 10
These are ten solutions to the equation.

If we plot these points on a coordinate plane, we will see that they all lie on a straight line.

Therefore the shape of the graph is a line. The equation represents a linear relationship between x and y.

Answer 2

A linear line downwards

Step-by-step explanation:

You change the equation to y = 5 - 1/2x and as x increases, y becomes a smaller number, making the line go downwards as x increases (so it kinda looks like a \ on a graph). To find 10 solutions, just plug in values for x and make coords, ie (1, 4.5) from y = 5 - 1/2.