What is the slope of [tex]6 x+3 y=15[/tex]?
Answer (2)
Rewrite the given equation 6 x + 3 y = 15 in slope-intercept form.
Isolate the y term: 3 y = − 6 x + 15 .
Divide by 3 to get y = − 2 x + 5 .
Identify the slope as the coefficient of x , which is − 2 .
Explanation
Understanding the Problem We are given the equation of a line: 6 x + 3 y = 15 . Our goal is to find the slope of this line.
Converting to Slope-Intercept Form To find the slope, we need to 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, let's isolate the term with y on one side of the equation: 3 y = − 6 x + 15
Solving for y Now, divide both sides of the equation by 3 to solve for y :
y = 3 − 6 x + 3 15 y = − 2 x + 5
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 -2.
Final Answer Therefore, the slope of the line 6 x + 3 y = 15 is − 2 .
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 responsive the quantity 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 design systems effectively in various fields.
The slope of the equation 6 x + 3 y = 15 is found by converting it to slope-intercept form, resulting in y = − 2 x + 5 . Thus, the slope is − 2 .
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