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.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the algebraic representation for the given table

00:04 Use the formula for representing a linear function

00:12 Substitute the point and solve for the unknown B

00:16 This is the Y-axis intersection point (unknown B)

00:20 Let's take 2 given points

00:26 Use the formula to find the slope using 2 points on the graph

00:30 Substitute appropriate values according to the data, and solve to find the slope

00:36 This is the graph's slope

00:39 Accordingly substitute the slope and intersection point to find the function

00:48 And this is the solution to the question

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

For the function in front of you, the slope is?

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.

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