Question

Week 4 - Math 8 - Assessment
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Question
Given the table for x, lawns mowed, and y, money earned:

x - # of lawns mowed 7 6 2 9 3
y - $ earned 294 252 84 378 126
Match the equation type with the correct equation for this table.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Standard form
Slope-intercept form
Point-Slope form

Answer 1

To match the equation types with the correct equation based on the given data in the table, we need to first determine the relationship between the variables \(x\) (the number of lawns mowed) and \(y\) (the money earned).

1. Identify the slope (\(m\)):
We can find the slope by using two points from the table. For example, let's use \( (2, 84) \) and \( (7, 294) \).

The slope \(m\) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{294 - 84}{7 - 2} = \frac{210}{5} = 42
\]

2. Write the Slope-Intercept Form (y = mx + b):
Using one of the points, say \( (2, 84) \):
\[
84 = 42(2) + b
\]
\[
84 = 84 + b \implies b = 0
\]
Therefore, the equation in slope-intercept form is:
\[
y = 42x
\]

3. Write the Point-Slope Form:
The point-slope form can be expressed as:
\[
y - y_1 = m(x - x_1)
\]
Using the point \( (2, 84) \):
\[
y - 84 = 42(x - 2)
\]

4. Write the Standard Form (Ax + By = C):
From \( y = 42x \), rearranging gives:
\[
-42x + y = 0 \quad or \quad 42x - y = 0 \quad (Standard form usually has A, B, C as integers)
\]

Now let's match the equation types with the forms:

1. **Standard form**: \( 42x - y = 0 \)
2. **Slope-intercept form**: \( y = 42x \)
3. **Point-Slope form**: \( y - 84 = 42(x - 2) \)

You can place the responses into the respective inputs as follows:

1. **Standard form**: 42x - y = 0
2. **Slope-intercept form**: y = 42x
3. **Point-Slope form**: y - 84 = 42(x - 2)