Find Points on y = 3/4x + 4: Linear Function Analysis

Q: Why can't I just look at the graph to find points?

While graphing helps visualize, algebraic verification is more accurate! Graphs can be imprecise, especially with fractional coordinates like $ \frac{35}{8} $. Always substitute to be certain.

Q: How do I work with these complicated fractions?

Take it step by step! First multiply the fractions: $ \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} $. Then add 4 by converting to eighths: $ \frac{3}{8} + \frac{32}{8} = \frac{35}{8} $.

Q: What if I get a different y-value than what's given?

That means the point does not lie on the function! For example, if substituting gives you $ y = 5 $ but the point shows $ y = 3 $, that point is not on the line.

Q: Why is the y-intercept important here?

The y-intercept is $ (0, 4) $ from our equation $ y = \frac{3}{4}x + 4 $. Notice that $ (0, 0) $ is not the y-intercept, so it can't be on our line!

Linear Functions with Point Verification

$y=\frac{3}{4}x+4$

Through which points does the above function pass?

❤️ 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

00:06 Let's find out which points the function passes through.

00:10 At each point, the left number is X, and the right number is Y.

00:15 Let's plug each point into the line equation to see if it works.

00:21 It doesn't work, so this point is not on the line.

00:25 We'll do the same for other points to see which ones lie on the line.

00:30 Now, let's check the second point by substituting it into the line equation.

00:37 This one doesn't work either, so it's not on the line.

00:41 Let's try the third point now and substitute it into the line equation.

00:58 It works! So, this point is on the line.

01:02 Finally, let's check the fourth point by substituting it into the line equation.

01:15 This point doesn't work, so it's not on the line.

01:19 And that's how we determine which points are on the line.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$y=\frac{3}{4}x+4$

Through which points does the above function pass?

Step-by-step solution

To determine which point the function $y = \frac{3}{4}x + 4$ passes through, we will evaluate the given choices:

Evaluate the function for $x = \frac{1}{2}$ :

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

$y = \frac{3}{8} + 4$

$y = \frac{3}{8} + \frac{32}{8}$

$y = \frac{35}{8}$

Thus, the coordinate $\left(\frac{1}{2}, \frac{35}{8}\right)$ lies on the graph.

Therefore, the function passes through the point $\left(\frac{1}{2}, \frac{35}{8}\right)$ .

Final Answer

$(\frac{1}{2},\frac{35}{8})$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace x with given coordinate to find y-value
Technique: For $x = \frac{1}{2}$ : $y = \frac{3}{4} \times \frac{1}{2} + 4 = \frac{35}{8}$
Check: Point lies on function when calculated y equals given y-coordinate ✓

Common Mistakes

Avoid these frequent errors

Testing only one coordinate of each point
Don't just check if the x-value seems reasonable = missing half the verification! You might pick a point that doesn't actually satisfy the equation. Always substitute the x-coordinate into the function and verify the resulting y-value matches exactly.

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

Why can't I just look at the graph to find points?

While graphing helps visualize, algebraic verification is more accurate! Graphs can be imprecise, especially with fractional coordinates like $\frac{35}{8}$ . Always substitute to be certain.

How do I work with these complicated fractions?

Take it step by step! First multiply the fractions: $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$ . Then add 4 by converting to eighths: $\frac{3}{8} + \frac{32}{8} = \frac{35}{8}$ .

What if I get a different y-value than what's given?

That means the point does not lie on the function! For example, if substituting gives you $y = 5$ but the point shows $y = 3$ , that point is not on the line.

Can I work backwards from the y-value?

Yes! You can substitute the y-coordinate and solve for x to double-check. If you get the same x-coordinate as given, the point is on the function.

Why is the y-intercept important here?

The y-intercept is $(0, 4)$ from our equation $y = \frac{3}{4}x + 4$ . Notice that $(0, 0)$ is not the y-intercept, so it can't be on our line!

🌟 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