What is the x-intercept of the line 3x - 2y = 12?
A. (0,-6)
B. (0,4)
C. (4,0)
D. (-6,0)
Answer (2)
Substitute y = 0 into the equation 3 x − 2 y = 12 .
Solve for x : 3 x = 12 , which gives x = 4 .
The x-intercept is the point where the line crosses the x-axis, so the y-coordinate is 0.
The x-intercept is ( 4 , 0 ) .
Explanation
Understanding the Problem We are given the equation of a line: 3 x − 2 y = 12 . We need to find the x-intercept of this line. Remember that the x-intercept is the point where the line crosses the x-axis, which means the y-coordinate of that point is 0.
Substituting y = 0 To find the x-intercept, we substitute y = 0 into the equation of the line: 3 x − 2 ( 0 ) = 12
Solving for x Now we solve for x : 3 x − 0 = 12 3 x = 12 x = 3 12 x = 4
Finding the x-intercept So, the x-intercept is the point ( 4 , 0 ) .
Final Answer Therefore, the x-intercept of the line 3 x − 2 y = 12 is ( 4 , 0 ) .
Examples
Understanding x-intercepts is crucial in many real-world applications. For example, if you are analyzing the cost of production, the x-intercept of the cost function represents the point where the cost is zero. Similarly, in physics, if you are analyzing the motion of an object, the x-intercept of the position function represents the time when the object is at the origin. Knowing how to find x-intercepts helps in interpreting data and making informed decisions in various fields.
The x-intercept of the line given by the equation 3 x − 2 y = 12 is the point ( 4 , 0 ) . This is found by substituting y = 0 into the equation and solving for x . Thus, the correct option is C. (4, 0).
;
