Of course! To compare the two linear functions, we need to look at their slopes and y-intercepts. Let's start by analyzing the first function:
### Function 1: [tex]\( y = -\frac{4}{5}x + 7 \)[/tex]
1. Slope: The coefficient of [tex]\(x\)[/tex] is [tex]\(-\frac{4}{5}\)[/tex]. This represents the slope of the line. The slope tells us how steep the line is and the direction in which it slopes. A negative slope of [tex]\(-\frac{4}{5}\)[/tex] means that the line slopes downward from left to right.
2. Y-intercept: The constant term is [tex]\(7\)[/tex]. This represents the y-intercept, which is the point where the line crosses the y-axis. Here, the line will cross the y-axis at the point [tex]\((0, 7)\)[/tex].
Now, we'll analyze Function 2. However, since Function 2 isn't provided, let's go through what is required to draw a comparison:
### Function 2:
To compare it effectively, we need to know:
1. Slope: The coefficient of [tex]\(x\)[/tex] in Function 2.
2. Y-intercept: The constant term or the point where Function 2 crosses the y-axis.
### General Comparison:
1. Comparing Slopes:
- If Function 2 has a slope less than [tex]\(-\frac{4}{5}\)[/tex], its line is steeper downhill (more negative slope).
- If Function 2 has a slope greater than [tex]\(-\frac{4}{5}\)[/tex] but still negative, its line is less steep downhill.
- If Function 2 has a positive slope, it slopes upward from left to right.
2. Comparing Y-intercepts:
- If Function 2's y-intercept is greater than [tex]\(7\)[/tex], it means Function 2 starts higher on the y-axis compared to Function 1.
- If Function 2's y-intercept is less than [tex]\(7\)[/tex], it means Function 2 starts lower on the y-axis compared to Function 1.
Without a specific equation for Function 2, we can't perform a precise comparison. If you provide the equation for Function 2, we could detail exactly how the two functions compare in terms of their slopes and intercepts.
