Graph: Y = 3 4 X + 5 Y=\frac{3}{4} X+5 Y = 4 3 ​ X + 5 Which Point Lies On The Graph Of The Line?A. (5, 8)B. (1, 6)C. (-3, 3)D. (-4, 2)

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Introduction

In mathematics, a graph is a visual representation of a set of points and the relationships between them. A line graph is a type of graph that represents a linear relationship between two variables, typically represented by the x-axis and y-axis. In this article, we will explore the graph of the line $y=\frac{3}{4} x+5$ and determine which point lies on the graph.

Understanding the Equation

The equation $y=\frac{3}{4} x+5$ represents a linear relationship between the variables x and y. The slope of the line is $\frac{3}{4}$, which means that for every unit increase in x, y increases by $\frac{3}{4}$ unit. The y-intercept of the line is 5, which means that the line intersects the y-axis at the point (0, 5).

Finding the Point that Lies on the Graph

To find the point that lies on the graph of the line, we need to substitute the x-coordinate of the point into the equation and solve for y. Let's examine each of the given options:

Option A: (5, 8)

Substituting x = 5 into the equation, we get:

$y = \frac{3}{4} (5) + 5$ $y = \frac{15}{4} + 5$ $y = 3.75 + 5$ $y = 8.75$

Since 8.75 is not equal to 8, option A is incorrect.

Option B: (1, 6)

Substituting x = 1 into the equation, we get:

$y = \frac{3}{4} (1) + 5$ $y = \frac{3}{4} + 5$ $y = 0.75 + 5$ $y = 5.75$

Since 5.75 is not equal to 6, option B is incorrect.

Option C: (-3, 3)

Substituting x = -3 into the equation, we get:

$y = \frac{3}{4} (-3) + 5$ $y = -\frac{9}{4} + 5$ $y = -2.25 + 5$ $y = 2.75$

Since 2.75 is not equal to 3, option C is incorrect.

Option D: (-4, 2)

Substituting x = -4 into the equation, we get:

$y = \frac{3}{4} (-4) + 5$ $y = -3 + 5$ $y = 2$

Since 2 is equal to 2, option D is correct.

Conclusion

In conclusion, the point that lies on the graph of the line $y=\frac{3}{4} x+5$ is option D: (-4, 2). This point satisfies the equation and lies on the graph of the line.

Key Takeaways

• A graph is a visual representation of a set of points and the relationships between them.
• A line graph represents a linear relationship between two variables.
• The slope of the line is $\frac{3}{4}$, which means that for every unit increase in x, y increases by $\frac{3}{4}$ unit.
• The y-intercept of the line is 5, which means that the line intersects the y-axis at the point (0, 5).
• To find the point that lies on the graph of the line, substitute the x-coordinate of the point into the equation and solve for y.

Further Reading

For more information on graphing lines and solving equations, check out the following resources:

• Khan Academy: Graphing Lines
• Mathway: Solving Equations
• Wolfram Alpha: Graphing and Solving Equations
  Graph: $y=\frac{3}{4} x+5$ - Q&A =====================================

Introduction

In our previous article, we explored the graph of the line $y=\frac{3}{4} x+5$ and determined which point lies on the graph. In this article, we will answer some frequently asked questions about the graph and provide additional information to help you better understand the concept.

Q&A

Q: What is the slope of the line?

A: The slope of the line is $\frac{3}{4}$, which means that for every unit increase in x, y increases by $\frac{3}{4}$ unit.

Q: What is the y-intercept of the line?

A: The y-intercept of the line is 5, which means that the line intersects the y-axis at the point (0, 5).

Q: How do I find the point that lies on the graph of the line?

A: To find the point that lies on the graph of the line, substitute the x-coordinate of the point into the equation and solve for y.

Q: What if I have a point that does not lie on the graph of the line?

A: If you have a point that does not lie on the graph of the line, it means that the point does not satisfy the equation. You can try substituting the x-coordinate of the point into the equation and solving for y to see if it matches the y-coordinate of the point.

Q: Can I graph the line using a calculator or computer software?

A: Yes, you can graph the line using a calculator or computer software. Many calculators and computer software programs have built-in graphing capabilities that allow you to enter the equation and view the graph.

Q: How do I determine the equation of a line given two points?

A: To determine the equation of a line given two points, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. You can find the slope by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Q: What is the significance of the graph of a line?

A: The graph of a line is a visual representation of the relationship between the variables x and y. It can be used to identify patterns and trends in data, and to make predictions about future values.

Conclusion

In conclusion, the graph of the line $y=\frac{3}{4} x+5$ is a useful tool for understanding the relationship between the variables x and y. By answering some frequently asked questions, we have provided additional information to help you better understand the concept.

Key Takeaways

• The slope of the line is $\frac{3}{4}$, which means that for every unit increase in x, y increases by $\frac{3}{4}$ unit.
• The y-intercept of the line is 5, which means that the line intersects the y-axis at the point (0, 5).
• To find the point that lies on the graph of the line, substitute the x-coordinate of the point into the equation and solve for y.
• You can graph the line using a calculator or computer software.
• The graph of a line is a visual representation of the relationship between the variables x and y.

Further Reading

For more information on graphing lines and solving equations, check out the following resources:

• Khan Academy: Graphing Lines
• Mathway: Solving Equations
• Wolfram Alpha: Graphing and Solving Equations

Additional Resources

• Graphing Calculator: A graphing calculator is a useful tool for graphing lines and other functions.
• Computer Software: Many computer software programs have built-in graphing capabilities that allow you to enter the equation and view the graph.
• Online Graphing Tools: There are many online graphing tools available that allow you to enter the equation and view the graph.