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?

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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

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Which statement best describes the graph below?

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!

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