Match the Function Equation: Analyzing X-Y Values from -3 to 5

Q: Which two points should I use from the table?

You can use any two points from the table! The slope will be the same regardless. Pick points that are easy to work with, like $ (-1,4) $ and $ (3,8) $.

Q: How do I find the y-intercept after calculating slope?

Substitute any point from the table and your slope into $ y = mx + b $. Then solve for b. For example: $ 8 = 1(3) + b $, so $ b = 5 $.

Q: What if I get a different slope using different points?

If you get different slopes, check your arithmetic! Linear functions have the same slope between any two points. Reread the table values carefully and recalculate.

Q: How can I verify my equation is correct?

Test your equation with all the points from the table. If $ y = x + 5 $ is correct, then (-3,2), (-1,4), (1,6), (3,8), and (5,10) should all work when substituted.

Linear Functions with Table Data

Which of the following equations corresponds to the function represented in the table?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's find the function equations using the given table.

00:17 First, we'll use the formula to find the graph's slope.

00:22 We'll plug in the right values from the data and calculate the slope.

00:32 Remember, negative times negative equals positive. Let's multiply.

00:37 Great! That's the slope of our graph.

00:45 Next, we'll use the line equation to find point B, the intersection.

00:52 Again, substitute the right values from the data to solve for B.

01:01 Let's isolate B in the equation.

01:08 Awesome! We found intersection point B.

01:12 Finally, substitute values into the line equation to get the full equation.

01:17 And that's how we solve this problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the following equations corresponds to the function represented in the table?

Step-by-step solution

We will begin by using the formula for finding slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

First let's take the points:

$(-1,4),(3,8)$

$m=\frac{8-4}{3-(-1)}=$

$\frac{8-4}{3+1}=$

$\frac{4}{4}=1$

Next we'll substitute the point and slope into the line equation:

$y=mx+b$

$8=1\times3+b$

$8=3+b$

Lastly we'll combine like terms:

$8-3=b$

$5=b$

Therefore, the equation will be:

$y=x+5$

Final Answer

$y=x+5$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use m = (y₂-y₁)/(x₂-x₁) with any two table points
Technique: Calculate slope: (8-4)/(3-(-1)) = 4/4 = 1
Check: Substitute any table point into y = x + 5 ✓

Common Mistakes

Avoid these frequent errors

Using incorrect coordinates from the table
Don't mix up x and y values or misread the table = wrong slope calculation! This leads to completely incorrect equations. Always double-check that you're reading coordinates as (x,y) pairs correctly from the table.

Practice Quiz

Test your knowledge with interactive questions

Is the given graph a function?

FAQ

Everything you need to know about this question

Which two points should I use from the table?

You can use any two points from the table! The slope will be the same regardless. Pick points that are easy to work with, like $(-1,4)$ and $(3,8)$ .

How do I find the y-intercept after calculating slope?

Substitute any point from the table and your slope into $y = mx + b$ . Then solve for b. For example: $8 = 1(3) + b$ , so $b = 5$ .

What if I get a different slope using different points?

If you get different slopes, check your arithmetic! Linear functions have the same slope between any two points. Reread the table values carefully and recalculate.

How can I verify my equation is correct?

Test your equation with all the points from the table. If $y = x + 5$ is correct, then (-3,2), (-1,4), (1,6), (3,8), and (5,10) should all work when substituted.

Why does the table show a linear relationship?

Look at the pattern: as x increases by 2, y increases by 2. This constant rate of change means the relationship is linear with slope = 1.

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