Find the slope of the line represented by the equation below.
[tex]2 y-5 x=-6[/tex]
Answer (2)
To find the slope of the line given by 2 y − 5 x = − 6 , we rearranged the equation into slope-intercept form, leading us to determine that the slope is 2 5 .
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Add 5 x to both sides of the equation: 2 y = 5 x − 6 .
Divide both sides by 2 to solve for y : y = 2 5 x − 3 .
Identify the slope m in the slope-intercept form y = m x + b .
The slope of the line is 2 5 .
Explanation
Understanding the Problem We are given the equation of a line: 2 y − 5 x = − 6 . 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 do this by adding 5 x to both sides of the equation: 2 y − 5 x + 5 x = − 6 + 5 x 2 y = 5 x − 6
Solving for y Next, we need to solve for y by dividing both sides of the equation by the coefficient of y , which is 2: 2 2 y = 2 5 x − 6 y = 2 5 x − 2 6 y = 2 5 x − 3
Identifying the Slope Now that the equation is in slope-intercept form, y = m x + b , we can identify the slope m . In this case, m = 2 5 . Therefore, the slope of the line is 2 5 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, in construction, the slope of a ramp determines its steepness and accessibility. In economics, the slope of a supply or demand curve indicates how sensitive the quantity supplied or demanded is to changes in price. In physics, the slope of a velocity-time graph represents acceleration. Knowing how to find the slope from an equation allows us to analyze and predict these relationships effectively.
