To determine which linear function has the steepest slope, we first need to identify the slope of each given linear equation.
1. For the equation [tex]\( y = -8x + 5 \)[/tex], the slope is directly given as [tex]\(-8\)[/tex].
2. For the equation [tex]\( y - 9 = -2(x + 1) \)[/tex], we need to put it into the slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
y - 9 = -2(x + 1)
\][/tex]
[tex]\[
y - 9 = -2x - 2
\][/tex]
[tex]\[
y = -2x + 7
\][/tex]
Here, the slope is [tex]\(-2\)[/tex].
3. For the equation [tex]\( y = 7x - 3 \)[/tex], the slope is directly given as [tex]\( 7 \)[/tex].
4. For the equation [tex]\( y + 2 = 6(x + 10) \)[/tex], we need to put it into the slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
y + 2 = 6(x + 10)
\][/tex]
[tex]\[
y + 2 = 6x + 60
\][/tex]
[tex]\[
y = 6x + 58
\][/tex]
Here, the slope is [tex]\( 6 \)[/tex].
Now, we have identified the slopes of each linear function:
- Slope of [tex]\( y = -8x + 5 \)[/tex] is [tex]\(-8\)[/tex]
- Slope of [tex]\( y - 9 = -2(x + 1) \)[/tex] is [tex]\(-2\)[/tex]
- Slope of [tex]\( y = 7x - 3 \)[/tex] is [tex]\(7\)[/tex]
- Slope of [tex]\( y + 2 = 6(x + 10) \)[/tex] is [tex]\(6\)[/tex]
To determine the steepest slope, we need to look at the absolute values of these slopes:
- [tex]\( |\text{slope}| \)[/tex] for [tex]\(-8\)[/tex] is [tex]\( 8 \)[/tex]
- [tex]\( |\text{slope}| \)[/tex] for [tex]\(-2\)[/tex] is [tex]\( 2 \)[/tex]
- [tex]\( |\text{slope}| \)[/tex] for [tex]\( 7 \)[/tex] is [tex]\( 7 \)[/tex]
- [tex]\( |\text{slope}| \)[/tex] for [tex]\( 6 \)[/tex] is [tex]\( 6 \)[/tex]
Comparing these absolute values, the largest one is [tex]\(8\)[/tex].
Therefore, the linear function with the steepest slope is [tex]\( y = -8x + 5 \)[/tex], which has a slope of [tex]\(-8\)[/tex].
