To determine which equation would make the graph of [tex]\( y = 6x + 7 \)[/tex] less steep, we need to analyze the slopes of the given equations. The steepness of a graph of a linear equation is determined by the absolute value of the slope, which is the coefficient of [tex]\( x \)[/tex].
The original equation is:
[tex]\[ y = 6x + 7 \][/tex]
Here, the slope is [tex]\( 6 \)[/tex].
Now, let's consider each of the given options:
- Option A: [tex]\( y = -6x + 7 \)[/tex]
- The slope is [tex]\( -6 \)[/tex]. The absolute value of the slope is [tex]\( 6 \)[/tex]. So, the steepness remains the same, but in the opposite direction.
- Option B: [tex]\( y = 6x + 4 \)[/tex]
- The slope is [tex]\( 6 \)[/tex]. The absolute value of the slope is still [tex]\( 6 \)[/tex]. Thus, the steepness of the graph does not change.
- Option C: [tex]\( y = 2x + 7 \)[/tex]
- The slope is [tex]\( 2 \)[/tex]. The absolute value of the slope is [tex]\( 2 \)[/tex]. This is less than [tex]\( 6 \)[/tex], meaning the graph is less steep compared to the original equation.
- Option D: [tex]\( y = 10x + 7 \)[/tex]
- The slope is [tex]\( 10 \)[/tex]. The absolute value of the slope is [tex]\( 10 \)[/tex]. This is greater than [tex]\( 6 \)[/tex], making the graph steeper.
Among the choices, the equation with the slope that makes the graph less steep is:
[tex]\[ y = 2x + 7 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
