Find the slope of the line: [tex]2 y-x-3=0$[/tex].
a. [tex]-1 / 2$[/tex]
b. -2
c. [tex]1 / 2$[/tex]
d. 2
Answer (2)
Rewrite the equation in slope-intercept form ( y = m x + b ).
Isolate y on one side of the equation: 2 y = x + 3 .
Divide both sides by 2: y = 2 1 x + 2 3 .
Identify the slope as the coefficient of x : 2 1 .
Explanation
Understanding the Problem We are given the equation of a line: 2 y − x − 3 = 0 . 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 y To rewrite the given equation in slope-intercept form, we need to isolate y on one side of the equation. First, we add x and 3 to both sides of the equation: 2 y − x − 3 + x + 3 = 0 + x + 3 2 y = x + 3
Slope-Intercept Form Next, we divide both sides of the equation by 2 :
2 2 y = 2 x + 3 y = 2 1 x + 2 3
Finding the Slope Now the equation is in the form y = m x + b . Comparing this to our result, y = 2 1 x + 2 3 , we can see that the coefficient of x is 2 1 . Therefore, the slope of the line is 2 1 .
Final Answer The slope of the line 2 y − x − 3 = 0 is 2 1 . Therefore, the correct answer is c. 2 1 .
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 allows us to analyze and design systems effectively in various fields.
The slope of the line represented by the equation 2 y − x − 3 = 0 is 2 1 . Therefore, the correct option is (c) 2 1 .
;
