Question

Which linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)

Answer 1

To determine which linear function has the steepest slope, we can identify the slope of each function from its standard form \(y = mx + b\), where \(m\) is the slope.

1. **First function:**
\[
y = -8x + 5
\]
- Slope \(m = -8\)

2. **Second function:**
\[
y - 9 = -2(x + 1)
\]
Start by simplifying it:
\[
y - 9 = -2x - 2 \implies y = -2x + 7
\]
- Slope \(m = -2\)

3. **Third function:**
\[
y = 7x - 3
\]
- Slope \(m = 7\)

4. **Fourth function:**
\[
y + 2 = 6(x + 10)
\]
Simplifying it:
\[
y + 2 = 6x + 60 \implies y = 6x + 58
\]
- Slope \(m = 6\)

Now let's summarize the slopes:
- First function: slope = -8
- Second function: slope = -2
- Third function: slope = 7
- Fourth function: slope = 6

To find the steepest slope, we look for the maximum value:
- The largest slope among these is \(7\) from the third function \(y = 7x - 3\).

So, the linear function with the steepest slope is **\(y = 7x - 3\)**.