Linear Function Table: Match Values (0,5), (1,6), (2,7) to Its Equation

Q: How do I find the slope from a table?

Pick any two points from the table and use slope = rise/run. From points (0,5) and (1,6): slope = $ \frac{6-5}{1-0} = 1 $. The y-values go up by 1, x-values go up by 1, so slope is 1.

Q: What if I get a negative slope?

That's totally normal! A negative slope means the line goes downhill (y decreases as x increases). Just make sure your calculation is correct by checking with a second pair of points.

Q: How do I know which point gives me the y-intercept?

The y-intercept is always where x = 0. Look in your table for the row where x equals zero - that y-value is your y-intercept. Here, when x = 0, y = 5, so b = 5.

Q: Can I use any two points to find the slope?

Yes! For linear functions, any two points will give you the same slope. Try (1,6) and (2,7): slope = $ \frac{7-6}{2-1} = 1 $ - same answer!

Q: What if my equation doesn't match any of the choices?

Double-check your slope calculation and y-intercept identification. Make sure you're reading the table correctly - x-values in top row, y-values in bottom row. Verify by testing one point in your equation.

Linear Functions with Table Data

Below is a table containing values for x and y. This tables represents a linear function.

Choose the equation that corresponds to the function.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find how to express the table using algebra.

00:13 We will use the formula for a linear function. Ready?

00:21 Now, put in the point and find the value of B.

00:25 B is where the line crosses the Y-axis.

00:30 Let's pick two points from the table.

00:35 Use the points to find the slope of the graph.

00:39 Put the data into the formula and calculate the slope.

00:45 Great! That's the slope of the graph.

00:49 Combine the slope and B to form the function.

00:57 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a table containing values for x and y. This tables represents a linear function.

Choose the equation that corresponds to the function.

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

Step 1: Find the slope $m$ .
Step 2: Use the slope and a point to find the $y$ -intercept $b$ .
Step 3: Write the linear equation.

Let's work through each step:

Step 1: Calculate the slope $m$ .
Using the points $(0, 5)$ and $(1, 6)$ , the slope $m$ is calculated as follows:

$m = \frac{6 - 5}{1 - 0} = \frac{1}{1} = 1$

Step 2: Use the slope ( $m = 1$ ) to find the $y$ -intercept $b$ .
We know from the point $(0, 5)$ that when $x = 0$ , $y = 5$ , which directly gives us the $y$ -intercept:

$b = 5$

Step 3: Form the equation of the line using $y = mx + b$ .
Substitute the found values into the equation:

$y = 1 \cdot x + 5$

Simplifying gives:

$y = x + 5$

Thus, the equation corresponding to the function is $y = x + 5$ .

Final Answer

$y=x+5$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Linear functions show constant rate of change
Slope Calculation: Use m = (6-5)/(1-0) = 1 from table points
Y-intercept Check: When x=0, y=5 confirms b=5 ✓

Common Mistakes

Avoid these frequent errors

Confusing slope sign or y-intercept value
Don't rush and pick y = -x + 5 or y = x - 5 = wrong equation! This happens when you miscalculate slope direction or misread the y-intercept from the table. Always double-check: slope = rise/run using two points, and y-intercept is the y-value when x = 0.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

How do I find the slope from a table?

Pick any two points from the table and use slope = rise/run. From points (0,5) and (1,6): slope = $\frac{6-5}{1-0} = 1$ . The y-values go up by 1, x-values go up by 1, so slope is 1.

What if I get a negative slope?

That's totally normal! A negative slope means the line goes downhill (y decreases as x increases). Just make sure your calculation is correct by checking with a second pair of points.

How do I know which point gives me the y-intercept?

The y-intercept is always where x = 0. Look in your table for the row where x equals zero - that y-value is your y-intercept. Here, when x = 0, y = 5, so b = 5.

Can I use any two points to find the slope?

Yes! For linear functions, any two points will give you the same slope. Try (1,6) and (2,7): slope = $\frac{7-6}{2-1} = 1$ - same answer!

What if my equation doesn't match any of the choices?

Double-check your slope calculation and y-intercept identification. Make sure you're reading the table correctly - x-values in top row, y-values in bottom row. Verify by testing one point in your equation.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime