At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Which of the following linear equations has the steepest slope?

A. [tex]y = \frac{2}{3} x + 4[/tex]
B. [tex]y = -2 x + 11[/tex]
C. [tex]y = \frac{1}{4} x + 7[/tex]
D. [tex]y = -7 x + 2[/tex]


Sagot :

To determine which of the given linear equations has the steepest slope, we need to evaluate the magnitude (absolute value) of the slopes of each equation and compare them. Let's break it down step-by-step for each equation:

1. Equation A: [tex]\( y = \frac{2}{3}x + 4 \)[/tex]
- The slope is [tex]\( \frac{2}{3} \)[/tex].
- The absolute value of this slope is [tex]\( \left| \frac{2}{3} \right| = 0.6666666666666666 \)[/tex].

2. Equation B: [tex]\( y = -2x + 11 \)[/tex]
- The slope is [tex]\( -2 \)[/tex].
- The absolute value of this slope is [tex]\( \left| -2 \right| = 2 \)[/tex].

3. Equation C: [tex]\( y = \frac{1}{4}x + 7 \)[/tex]
- The slope is [tex]\( \frac{1}{4} \)[/tex].
- The absolute value of this slope is [tex]\( \left| \frac{1}{4} \right| = 0.25 \)[/tex].

4. Equation D: [tex]\( y = -7x + 2 \)[/tex]
- The slope is [tex]\( -7 \)[/tex].
- The absolute value of this slope is [tex]\( \left| -7 \right| = 7 \)[/tex].

Now, we compare the absolute values of the slopes:

- [tex]\( \left| \frac{2}{3} \right| = 0.6666666666666666 \)[/tex]
- [tex]\( \left| -2 \right| = 2 \)[/tex]
- [tex]\( \left| \frac{1}{4} \right| = 0.25 \)[/tex]
- [tex]\( \left| -7 \right| = 7 \)[/tex]

Among these, the largest absolute value is [tex]\( 7 \)[/tex]. Hence, the equation with the steepest slope is:

D. [tex]\( y = -7x + 2 \)[/tex]