Select The Correct Answer.Find The Slope And The { Y$}$-intercept Of The Equation ${ 4x + 5y = -9\$} .A. Slope { =\frac{4}{5}$}$ And { Y$}$-intercept { =-\frac{9}{5}$}$B. Slope

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Introduction

In mathematics, linear equations are a fundamental concept that plays a crucial role in various fields, including algebra, geometry, and calculus. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on finding the slope and y-intercept of a linear equation in the form of Ax + By = C, where A, B, and C are constants.

What is Slope and Y-Intercept?

The slope of a linear equation is a measure of how steep the line is, while the y-intercept is the point at which the line intersects the y-axis. The slope is denoted by the letter 'm' and is calculated as the change in y divided by the change in x. The y-intercept is denoted by the letter 'b' and is the value of y when x is equal to 0.

Finding Slope and Y-Intercept

To find the slope and y-intercept of a linear equation, we need to rewrite the equation in the form of y = mx + b, where m is the slope and b is the y-intercept. We can do this by isolating y on one side of the equation.

Step 1: Isolate y

Let's take the given equation 4x + 5y = -9 as an example. To isolate y, we need to get rid of the term 4x on the left-hand side of the equation.

# Given equation: 4x + 5y = -9
# Isolate y
y = (-4x - 9) / 5

Step 2: Rewrite the Equation

Now that we have isolated y, we can rewrite the equation in the form of y = mx + b.

# Rewrite the equation
y = (-4/5)x - 9/5

Step 3: Identify Slope and Y-Intercept

From the rewritten equation, we can see that the slope (m) is -4/5 and the y-intercept (b) is -9/5.

Conclusion

In this article, we have learned how to find the slope and y-intercept of a linear equation in the form of Ax + By = C. We have also seen how to isolate y and rewrite the equation in the form of y = mx + b. By following these steps, we can easily find the slope and y-intercept of any linear equation.

Answer

Based on the steps we have followed, the correct answer is:

A. Slope = -4/5 and y-intercept = -9/5

Discussion

  • What is the significance of slope and y-intercept in linear equations?
  • How do you isolate y in a linear equation?
  • What is the difference between slope and y-intercept?
  • Can you give an example of a linear equation and find its slope and y-intercept?

Related Topics

  • Linear Equations
  • Graphing Linear Equations
  • Slope and Y-Intercept
  • Linear Functions

References

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of Ax + By = C, where A, B, and C are constants.

Q: What is the significance of slope and y-intercept in linear equations?

A: The slope of a linear equation is a measure of how steep the line is, while the y-intercept is the point at which the line intersects the y-axis. The slope is denoted by the letter 'm' and is calculated as the change in y divided by the change in x. The y-intercept is denoted by the letter 'b' and is the value of y when x is equal to 0.

Q: How do you isolate y in a linear equation?

A: To isolate y, we need to get rid of the term Ax on the left-hand side of the equation. We can do this by subtracting Ax from both sides of the equation.

Q: What is the difference between slope and y-intercept?

A: The slope is a measure of how steep the line is, while the y-intercept is the point at which the line intersects the y-axis.

Q: Can you give an example of a linear equation and find its slope and y-intercept?

A: Let's take the equation 4x + 5y = -9 as an example. To find the slope and y-intercept, we need to isolate y.

# Given equation: 4x + 5y = -9
# Isolate y
y = (-4x - 9) / 5

From the rewritten equation, we can see that the slope (m) is -4/5 and the y-intercept (b) is -9/5.

Q: How do you graph a linear equation?

A: To graph a linear equation, we need to find two points on the line and plot them on a coordinate plane. We can then draw a line through the two points to represent the linear equation.

Q: What is the equation of a line in slope-intercept form?

A: The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Q: Can you give an example of a linear equation in slope-intercept form?

A: Let's take the equation y = -2x + 3 as an example. In this equation, the slope (m) is -2 and the y-intercept (b) is 3.

Q: How do you find the equation of a line given two points?

A: To find the equation of a line given two points, we need to find the slope of the line and then use the point-slope form of a linear equation.

Q: What is the point-slope form of a linear equation?

A: The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Q: Can you give an example of finding the equation of a line given two points?

A: Let's take the points (2, 3) and (4, 5) as an example. To find the equation of the line, we need to find the slope of the line and then use the point-slope form of a linear equation.

# Given points: (2, 3) and (4, 5)
# Find the slope
m = (5 - 3) / (4 - 2)
m = 1

y - 3 = 1(x - 2)
y - 3 = x - 2
y = x - 2 + 3
y = x + 1

From the rewritten equation, we can see that the equation of the line is y = x + 1.

Conclusion

In this article, we have answered some common questions about solving linear equations. We have also seen how to isolate y, find the slope and y-intercept, graph a linear equation, and find the equation of a line given two points. By following these steps, we can easily solve linear equations and find the equation of a line.