Question

Use the table to answer the question..

Table of Values

x
ya
yb
0 3 −2
1 5 1
2 7 4
Which system of linear equations is represented by the table of values?

(1 point)
Responses

{y=3x+2y=−2x+3

{y=−2x+3y=−3x−2

{y=2x+3y=3x−2

{y=2x−2y=3x+3

Answer 1

Use the image to answer the question.

Two lines intersect on the coordinate plane. Both axes range from negative 10 to 10 in increments of 1.

What is the system of equations shown in the graph?

(2 points)
The equation of the solid line is y=

x
.

The equation of the dotted line is y=

x
+
.

Answer 2

To find the system of linear equations represented by the table of values, we can analyze the points provided in the table.

The table contains the following points:
- For \(x = 0\), \(y_a = 3\) and \(y_b = -2\)
- For \(x = 1\), \(y_a = 5\) and \(y_b = 1\)
- For \(x = 2\), \(y_a = 7\) and \(y_b = 4\)

Now let's determine the equations for both sets of y-values (ya and yb).

### Finding the first equation (ya)

Using the points (0, 3), (1, 5), and (2, 7):

1. **Slope (m)**:
- The slope \(m\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using points (0, 3) and (1, 5):
\[
m = \frac{5 - 3}{1 - 0} = 2
\]

2. **Equation form**:
We can use the slope-intercept form \(y = mx + b\) and plug in one of the points to find \(b\). Using the point (0, 3):
\[
3 = 2(0) + b \implies b = 3
\]
Thus, the equation for \(y_a\) is:
\[
y_a = 2x + 3
\]

### Finding the second equation (yb)

Using the points (0, -2), (1, 1), and (2, 4):

1. **Slope (m)**:
Using points (0, -2) and (1, 1):
\[
m = \frac{1 - (-2)}{1 - 0} = 3
\]

2. **Equation form**:
Using the slope-intercept form \(y = mx + b\) with point (0, -2):
\[
-2 = 3(0) + b \implies b = -2
\]
Thus, the equation for \(y_b\) is:
\[
y_b = 3x - 2
\]

### The system of equations:

So the two equations representing the values in the table are:
- \(y_a = 2x + 3\)
- \(y_b = 3x - 2\)

None of the provided options exactly match this, but we can rewrite the equations based on the provided choices:

- The first equation \(y = 2x + 3\) corresponds to Option 3 \({y=2x+3}\).
- The second equation does not match with any of the provided options correctly.

However, since the equations we derived are:
1. \(y = 2x + 3\)
2. \(y = 3x - 2\)

That aligns with the option **{y=2x+3, y=3x−2}** as the best fit from the given options.

Answer 3

To determine the system of equations represented by the graph of two intersecting lines, we need specific information about the intercepts and slopes of the lines, which I can't directly analyze from an image. However, I can guide you on how to derive the equations if you can describe the graph or provide the intersection points and slopes.

### Steps to Determine the Equations:

1. **Identify the Solid Line:**
- Find at least two points on the solid line. For example, if the solid line passes through points (1, 2) and (2, 4), you can determine the slope (m) by using the formula
\[
m = \frac{y_2 - y_1}{x_2 - x_1}.
\]
- Then use point-slope form to write the equation for the line.

2. **Identify the Dotted Line:**
- Similarly, for the dotted line, find at least two points. For example, if it passes through (0, 1) and (2, 3), calculate its slope and then use the point-slope form to find the equation.

3. **Form of the Equations:**
- The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Once you gather this information, you can fill in the blanks as follows:

- The equation of the solid line is \(y = mx\) (you'll replace \(m\) with the actual slope).
- The equation of the dotted line is \(y = mx + b\) (replace \(m\) with the slope you calculated and \(b\) with the y-intercept).

If you provide specific points or values from the graph, I can help you solve for the exact equations!