Let's solve this question step-by-step.
1. The slope of a linear equation in the form [tex]\( y = mx + b \)[/tex] is the coefficient [tex]\( m \)[/tex].
2. Identify the slopes of the given equations:
- For equation [tex]\( A \)[/tex]: [tex]\( y = -7x + 2 \)[/tex]
- The slope is [tex]\( -7 \)[/tex].
- For equation [tex]\( B \)[/tex]: [tex]\( y = \frac{2}{3}x + 4 \)[/tex]
- The slope is [tex]\( \frac{2}{3} \)[/tex].
- For equation [tex]\( C \)[/tex]: [tex]\( y = \frac{1}{4}x + 7 \)[/tex]
- The slope is [tex]\( \frac{1}{4} \)[/tex].
- For equation [tex]\( D \)[/tex]: [tex]\( y = -2x + 11 \)[/tex]
- The slope is [tex]\( -2 \)[/tex].
3. Compare the absolute values of the slopes to determine the steepest slope:
- Absolute value of slope [tex]\( A \)[/tex]: [tex]\( |-7| = 7 \)[/tex]
- Absolute value of slope [tex]\( B \)[/tex]: [tex]\( \left|\frac{2}{3}\right| \approx 0.67 \)[/tex]
- Absolute value of slope [tex]\( C \)[/tex]: [tex]\( \left|\frac{1}{4}\right| = 0.25 \)[/tex]
- Absolute value of slope [tex]\( D \)[/tex]: [tex]\( |-2| = 2 \)[/tex]
4. The largest absolute value indicates the steepest slope.
Therefore, comparing the absolute values [tex]\( 7 \)[/tex], [tex]\( 0.67 \)[/tex], [tex]\( 0.25 \)[/tex], and [tex]\( 2 \)[/tex], the largest number is [tex]\( 7 \)[/tex].
So, the linear equation with the steepest slope is:
[tex]\[ A. \, y = -7x + 2 \][/tex]
