What is the slope of the line 3x – 4y = 12? ( ) A. 3 B. 34 C. 43 D. -43 E. -34
The correct Answer and Explanation is:
The equation of the line given is:
3x−4y=123x – 4y = 12
To determine the slope, we need to rewrite the equation in slope-intercept form, which is:
y=mx+by = mx + b
where m represents the slope.
Step 1: Solve for yy
Start by isolating yy:
−4y=−3x+12-4y = -3x + 12
Divide everything by -4:
y=34x−3y = \frac{3}{4}x – 3
Step 2: Identify the slope
Comparing with y=mx+by = mx + b, we see that m = \frac{3}{4}.
Since none of the answer choices directly match 34\frac{3}{4}, let’s analyze the given options. If there was an error in listing the choices, the closest correct representation would be 3/4, which is equivalent to 0.75.
Explanation:
The slope of a line represents the rate at which yy changes for every unit change in xx. In this case, the slope is 3/4, meaning for every 4 units moved horizontally (in the xx-direction), the line moves 3 units up (in the yy-direction).
Slope determines whether a line is increasing or decreasing:
- Positive slope (34\frac{3}{4}) means the line rises as xx increases.
- Negative slope (such as -3/4) would indicate a falling line.
Since none of the options match 34\frac{3}{4}, there might be an error in the multiple-choice values given.the correct slope is 34\frac{3}{4}.
