Which equation has the least steep graph?

A. [tex] y=\frac{1}{2}x + 2 [/tex]

B. [tex] y=-\frac{3}{4}x + 5 [/tex]

C. [tex] y=-10x - 8 [/tex]

D. [tex] y=4x - 3 [/tex]



Answer :

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]