Use Slope-intercept Form To Write The Equation Of The Line With The Given Properties.Given:- Slope M = − 7 M = -7 M = − 7 - Passing Through The Point ( 7 , 7 (7, 7 ( 7 , 7 ] Y = M X + B Y = Mx + B Y = M X + B Calculate B B B Using The Point ( 7 , 7 (7, 7 ( 7 , 7 ]:$7 =

Introduction

In mathematics, the slope-intercept form is a fundamental concept used to write the equation of a line. This form is represented as $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. In this article, we will explore how to use the slope-intercept form to write the equation of a line with a given slope and a point through which the line passes.

Understanding the Slope-Intercept Form

The slope-intercept form is a powerful tool for writing linear equations. It allows us to easily identify the slope and y-intercept of a line, making it a fundamental concept in algebra and geometry. The slope-intercept form is represented as $y = mx + b$, where:

• $m$ is the slope of the line
• $b$ is the y-intercept of the line

Given Properties

In this problem, we are given the following properties:

• Slope $m = -7$
• Passing through the point $(7, 7)$

Using the Point-Slope Form to Find the Equation

To find the equation of the line, we can use the point-slope form, which is represented as $y - y_1 = m(x - x_1)$. We can plug in the given point $(7, 7)$ and the slope $m = -7$ into this equation to get:

$y - 7 = -7(x - 7)$

Simplifying the Equation

To simplify the equation, we can expand the right-hand side and combine like terms:

$y - 7 = -7x + 49$

Adding 7 to Both Sides

To isolate $y$, we can add 7 to both sides of the equation:

$y = -7x + 56$

Conclusion

In this article, we used the slope-intercept form to write the equation of a line with a given slope and a point through which the line passes. We started with the point-slope form and simplified the equation to get the final result. The equation of the line is $y = -7x + 56$. This equation represents a line with a slope of -7 and a y-intercept of 56.

Discussion

The slope-intercept form is a powerful tool for writing linear equations. It allows us to easily identify the slope and y-intercept of a line, making it a fundamental concept in algebra and geometry. In this problem, we used the point-slope form to find the equation of the line, and then simplified the equation to get the final result. This problem demonstrates the importance of using the slope-intercept form to write the equation of a line.

Example Problems

Here are a few example problems that demonstrate the use of the slope-intercept form:

• Find the equation of a line with a slope of 3 and a y-intercept of 2.
• Find the equation of a line with a slope of -2 and a point through which the line passes (4, 6).
• Find the equation of a line with a slope of 1 and a y-intercept of 5.

Solutions

Here are the solutions to the example problems:

• $y = 3x + 2$
• $y = -2x + 10$
• $y = x + 5$

Conclusion

In conclusion, the slope-intercept form is a powerful tool for writing linear equations. It allows us to easily identify the slope and y-intercept of a line, making it a fundamental concept in algebra and geometry. In this article, we used the slope-intercept form to write the equation of a line with a given slope and a point through which the line passes. We started with the point-slope form and simplified the equation to get the final result. The equation of the line is $y = -7x + 56$. This equation represents a line with a slope of -7 and a y-intercept of 56.