Test Questions: Writing Linear Equations from Tables (Grade 8)

📚 Quick Study Guide

• 📈 Slope-Intercept Form: A linear equation can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• ➗ Calculating Slope (m): Given two points $(x_1, y_1)$ and $(x_2, y_2)$ from the table, the slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• 📍 Finding the y-intercept (b): Once you have the slope, substitute the value of $m$ and the coordinates of any point $(x, y)$ from the table into the equation $y = mx + b$ and solve for $b$.
• 📝 Writing the Equation: After finding both $m$ and $b$, plug these values into the slope-intercept form $y = mx + b$ to get the linear equation.
• ➕ Checking your work: Choose another point on the table and substitute the x and y values into your equation. Make sure it is balanced to confirm it is correct.

Practice Quiz

1. What is the slope of the line represented by the following table?

   x	y
   1	5
   2	8
   3	11

   1. 0
   2. 1
   3. 3
   4. 5
2. What is the y-intercept of the line represented by the following table?

   x	y
   0	2
   1	5
   2	8

   1. 0
   2. 1
   3. 2
   4. 3
3. Which equation represents the relationship shown in the table?

   x	y
   1	-1
   2	1
   3	3

   1. y = x + 2
   2. y = 2x - 3
   3. y = 3x - 4
   4. y = x - 2
4. What is the equation of the line for the values shown?

   x	y
   -1	-5
   0	-2
   1	1

   1. y = 3x - 2
   2. y = -2x + 3
   3. y = 3x + 2
   4. y = 2x - 3
5. Which table of values represents the equation $y = -x + 4$?

   1. x	y
      1	5
      2	6
      3	7

   2. x	y
      1	3
      2	2
      3	1

   3. x	y
      -1	3
      0	2
      1	1

   4. x	y
      -1	5
      0	4
      1	3

6. Given the table, what is the value of y when x = 5?

   x	y
   0	1
   1	3
   2	5

   1. 7
   2. 9
   3. 11
   4. 13
7. Find the equation that represents the following table:

   x	y
   2	1
   4	2
   6	3

   1. $y = \frac{1}{2}x$
   2. $y = 2x$
   3. $y = x + 1$
   4. $y = \frac{1}{2}x + 1$