To determine which equation has the least steep graph, we need to compare the steepness of each line. The steepness of a line is determined by the absolute value of its slope. Here are the equations given:
A. [tex]\( y = \frac{1}{4} x + 6 \)[/tex]
B. [tex]\( y = -\frac{3}{4} x - 9 \)[/tex]
C. [tex]\( y = -7 x - 2 \)[/tex]
D. [tex]\( y = 2 x + 1 \)[/tex]
First, identify the slope for each equation:
- For equation A, [tex]\( y = \frac{1}{4} x + 6 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\( \frac{1}{4} \)[/tex].
- For equation B, [tex]\( y = -\frac{3}{4} x - 9 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\( -\frac{3}{4} \)[/tex].
- For equation C, [tex]\( y = -7 x - 2 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\( -7 \)[/tex].
- For equation D, [tex]\( y = 2 x + 1 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\( 2 \)[/tex].
Next, we find the absolute value of each slope to determine the steepness:
- For equation A: [tex]\( |\frac{1}{4}| = 0.25 \)[/tex].
- For equation B: [tex]\( |-\frac{3}{4}| = 0.75 \)[/tex].
- For equation C: [tex]\( |-7| = 7 \)[/tex].
- For equation D: [tex]\( |2| = 2 \)[/tex].
Now, compare the absolute values:
- Steepness for equation A: [tex]\( 0.25 \)[/tex]
- Steepness for equation B: [tex]\( 0.75 \)[/tex]
- Steepness for equation C: [tex]\( 7 \)[/tex]
- Steepness for equation D: [tex]\( 2 \)[/tex]
The least steep graph corresponds to the smallest absolute value of the slope. Here, the smallest value among [tex]\( 0.25 \)[/tex], [tex]\( 0.75 \)[/tex], [tex]\( 7 \)[/tex], and [tex]\( 2 \)[/tex] is [tex]\( 0.25 \)[/tex].
Thus, the equation with the least steep graph is:
A. [tex]\( y = \frac{1}{4} x + 6 \)[/tex]
