Helaine graphed the equation [tex]12 x-4 y=3[/tex]. What was the slope of Helaine's line?
Answer (2)
The slope of Helaine's line, given by the equation 12 x − 4 y = 3 , is 3 after rewriting it in slope-intercept form. The process involves isolating the y variable and identifying the coefficient of x as the slope. Therefore, the slope is 3 .
;
Rewrite the given equation 12 x − 4 y = 3 in slope-intercept form.
Isolate the y term: − 4 y = − 12 x + 3 .
Divide by − 4 to get y = 3 x − 4 3 .
Identify the slope as the coefficient of x , which is 3 .
Explanation
Understanding the Problem We are given the equation of a line 12 x − 4 y = 3 and asked to find its slope. 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 y term. Subtract 12 x from both sides of the equation: 12 x − 4 y − 12 x = 3 − 12 x − 4 y = − 12 x + 3
Solving for y Next, divide both sides of the equation by − 4 to solve for y :
− 4 − 4 y = − 4 − 12 x + 3 y = − 4 − 12 x + − 4 3 y = 3 x − 4 3
Identifying the Slope Now that the equation is in slope-intercept form, y = 3 x − 4 3 , we can identify the slope m . In this case, m = 3 .
Final Answer The slope of Helaine's line is 3.
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, if you are analyzing the steepness of a hill on a hiking trail, the slope tells you how much the altitude changes for every unit of horizontal distance. Similarly, in economics, the slope of a supply or demand curve indicates how the quantity of a product changes with its price. Knowing how to find and interpret the slope helps in making informed decisions in various fields.
