To determine which function has the steeper slope, we first need to determine the slopes of both functions.
Function 1:
- Given intercept points: [tex]\( (3,0) \)[/tex] and [tex]\( (0,4) \)[/tex].
- The formula to calculate the slope [tex]\( m \)[/tex] between 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]
- Substitute the given points:
[tex]\[ m_1 = \frac{4 - 0}{0 - 3} = \frac{4}{-3} = -\frac{4}{3} \][/tex]
Function 2:
- Given points: [tex]\((-12, -4), (-8, -1), (-4, 2), (0, 5), (4, 8)\)[/tex].
- To calculate the slope, we can use the first and the last points: [tex]\((-12, -4)\)[/tex] and [tex]\((4, 8)\)[/tex].
- Use the same slope formula:
[tex]\[ m_2 = \frac{8 - (-4)}{4 - (-12)} = \frac{8 + 4}{4 + 12} = \frac{12}{16} = \frac{3}{4} \][/tex]
Comparing the slopes:
- The slope of Function 1 is [tex]\(-\frac{4}{3}\)[/tex].
- The slope of Function 2 is [tex]\(\frac{3}{4}\)[/tex].
To determine which function has the steeper slope, we compare the absolute values of the slopes:
- Absolute value of slope of Function 1:
[tex]\[ \left| -\frac{4}{3} \right| = \frac{4}{3} = 1.333\][/tex]
- Absolute value of slope of Function 2:
[tex]\[ \left| \frac{3}{4} \right| = \frac{3}{4} = 0.75 \][/tex]
Since [tex]\( \frac{4}{3} > \frac{3}{4} \)[/tex] (or 1.333 > 0.75), Function 1 has the steeper slope.
So, the correct answer is:
D. Function 1 has a steeper slope of [tex]\(-\frac{4}{3}\)[/tex].
