To determine which equation has the least steep graph, we need to compare the slopes of each equation. The steepness of a line in a graph is determined by the absolute value of its slope. Let's analyze each equation step-by-step.
Equation A: [tex]\( y = \frac{1}{2} x + 2 \)[/tex]
The slope (m) of this equation is [tex]\(\frac{1}{2}\)[/tex].
Equation B: [tex]\( y = -\frac{3}{4} x + 5 \)[/tex]
The slope (m) of this equation is [tex]\(-\frac{3}{4}\)[/tex].
Equation C: [tex]\( y = -10 x - 8 \)[/tex]
The slope (m) of this equation is [tex]\(-10\)[/tex].
Equation D: [tex]\( y = 4 x - 3 \)[/tex]
The slope (m) of this equation is [tex]\(4\)[/tex].
Now, let's find the absolute values of these slopes to compare their steepness:
- For Equation A: [tex]\(|\frac{1}{2}| = 0.5\)[/tex]
- For Equation B: [tex]\(|-\frac{3}{4}| = 0.75\)[/tex]
- For Equation C: [tex]\(|-10| = 10\)[/tex]
- For Equation D: [tex]\(|4| = 4\)[/tex]
When we compare these absolute values:
- [tex]\(0.5\)[/tex]
- [tex]\(0.75\)[/tex]
- [tex]\(10\)[/tex]
- [tex]\(4\)[/tex]
The smallest absolute value is [tex]\(0.5\)[/tex], which corresponds to Equation A: [tex]\( y = \frac{1}{2} x + 2 \)[/tex].
Therefore, the equation with the least steep graph is:
A. [tex]\( y = \frac{1}{2} x + 2 \)[/tex]
