Question

Three points for equation 2y=5x+11

Answer 1

To determine three points for the equation 2y=5x+11, we rearranged the equation to slope-intercept form (y=(5/2)x+11/2) and chose values for x to calculate corresponding y values. The points obtained are (0, 11/2), (2, 21/2), and (-2, 1/2), which lie on the line described by the given equation.

Step-by-step explanation:

The student's question is asking for three points that would satisfy the equation 2y = 5x + 11. To find these points, we should first rearrange the equation into the slope-intercept form, which is y = mx + b. In this form, m represents the slope and b represents the y-intercept. The given equation can be rewritten as y = (5/2)x + 11/2. Now that we have the equation in slope-intercept form, we can easily find points by choosing values for x and solving for y.

Let's calculate three points:

1. For x = 0: y = (5/2)(0) + 11/2 = 11/2, so the point is (0, 11/2).
2. For x = 2: y = (5/2)(2) + 11/2 = 10 + 11/2 = 21/2, so the point is (2, 21/2).
3. For x = -2: y = (5/2)(-2) + 11/2 = -10 + 11/2 = 1/2, so the point is (-2, 1/2).

With these calculations, we've successfully identified three distinct points that lie on the line described by the equation 2y = 5x + 11.

Answer 2

Since this is a linear equation, (you can tell because there aren't any exponents) you technically only need to find two points to determine the line.

Anyways, here is how we can find points.
1. Choose a value to use for x.
2. Plug this into the eqn.
3. Solve for y.
4. Plot this point (x, y).

Let's try x = 0.
2y = 5(0) + 11
2y = 11
y = 5.5

Let's try x = 1.
2y = 5(1) + 11
2y = 5 + 11
2y = 16
y = 8

Let's try x = 2.
2y = 5(2) + 11
2y = 10 + 11
2y = 21
y = 10.5

Here are our three points: (0, 5.5), (1, 8), and (2, 10.5).
Plot these on a graph and just connect them using a ruler.