Find the slope of the line represented by the equation below:
10 = 5y - 4x

The slope of the line represented by the equation 10 = 5 y − 4 x can be found by rewriting it in slope-intercept form to get y = 5 4 ​ x + 2 , which shows that the slope is 5 4 ​ .
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Answered by Anonymous | 2025-07-04

Rewrite the given equation 10 = 5 y − 4 x in slope-intercept form.
Isolate 5 y to get 5 y = 4 x + 10 .
Divide by 5 to solve for y : y = 5 4 ​ x + 2 .
Identify the slope as the coefficient of x , which is 5 4 ​ ​ .

Explanation

Understanding the Problem We are given the equation of a line: 10 = 5 y − 4 x . Our goal is to find the slope of this line. To do this, we will rewrite the equation in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept.

Isolating the y-term First, we want to isolate the term with y on one side of the equation. We can rewrite the equation as: 5 y = 4 x + 10

Solving for y Next, we solve for y by dividing both sides of the equation by 5: y = 5 4 ​ x + 5 10 ​ y = 5 4 ​ x + 2

Identifying the Slope Now that the equation is in slope-intercept form, y = m x + b , we can identify the slope m as the coefficient of x . In this case, the slope is 5 4 ​ .

Final Answer Therefore, the slope of the line represented by the equation 10 = 5 y − 4 x is 5 4 ​ .


Examples
Understanding the slope of a line is crucial in many real-world applications. For example, if you are analyzing the relationship between the number of hours studied and the score on a test, the slope of the line would represent the average increase in score for each additional hour of studying. Similarly, in construction, the slope of a ramp determines its steepness, which is essential for accessibility. Linear relationships are fundamental in economics, physics, and engineering, making the ability to find and interpret slope a valuable skill.

Answered by GinnyAnswer | 2025-07-04