Answer :
Let's determine the slope of each function and see which one is steeper.
### Function 1:
Given points:
- [tex]\(x\)[/tex]-intercept: [tex]\((3, 0)\)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\((0, 4)\)[/tex]
The formula for the slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Applying the given points to the slope formula:
[tex]\[ m_1 = \frac{4 - 0}{0 - 3} = \frac{4}{-3} = -\frac{4}{3} \][/tex]
So, the slope of Function 1 is [tex]\(-\frac{4}{3}\)[/tex].
### Function 2:
Given the points:
[tex]\((-12, -4)\)[/tex] and [tex]\((-8, -1)\)[/tex]
Using the slope formula for these points:
[tex]\[ m_2 = \frac{-1 - (-4)}{-8 - (-12)} = \frac{-1 + 4}{-8 + 12} = \frac{3}{4} \][/tex]
So, the slope of Function 2 is [tex]\(\frac{3}{4}\)[/tex].
### Comparison:
To determine which slope is steeper, we compare the absolute values of the slopes:
[tex]\[ |\text{slope of Function 1}| = \left|-\frac{4}{3}\right| = \frac{4}{3} \][/tex]
[tex]\[ |\text{slope of Function 2}| = \left|\frac{3}{4}\right| = \frac{3}{4} \][/tex]
Since [tex]\(\frac{4}{3}\)[/tex] is greater than [tex]\(\frac{3}{4}\)[/tex], the slope of Function 1 is steeper.
Thus, the correct answer is:
C. Function 1 has a steeper slope of [tex]\(-\frac{4}{3}\)[/tex].
### Function 1:
Given points:
- [tex]\(x\)[/tex]-intercept: [tex]\((3, 0)\)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\((0, 4)\)[/tex]
The formula for the slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Applying the given points to the slope formula:
[tex]\[ m_1 = \frac{4 - 0}{0 - 3} = \frac{4}{-3} = -\frac{4}{3} \][/tex]
So, the slope of Function 1 is [tex]\(-\frac{4}{3}\)[/tex].
### Function 2:
Given the points:
[tex]\((-12, -4)\)[/tex] and [tex]\((-8, -1)\)[/tex]
Using the slope formula for these points:
[tex]\[ m_2 = \frac{-1 - (-4)}{-8 - (-12)} = \frac{-1 + 4}{-8 + 12} = \frac{3}{4} \][/tex]
So, the slope of Function 2 is [tex]\(\frac{3}{4}\)[/tex].
### Comparison:
To determine which slope is steeper, we compare the absolute values of the slopes:
[tex]\[ |\text{slope of Function 1}| = \left|-\frac{4}{3}\right| = \frac{4}{3} \][/tex]
[tex]\[ |\text{slope of Function 2}| = \left|\frac{3}{4}\right| = \frac{3}{4} \][/tex]
Since [tex]\(\frac{4}{3}\)[/tex] is greater than [tex]\(\frac{3}{4}\)[/tex], the slope of Function 1 is steeper.
Thus, the correct answer is:
C. Function 1 has a steeper slope of [tex]\(-\frac{4}{3}\)[/tex].
