To determine which equation has the steepest graph, we need to look at the slopes of the linear equations provided. The slope of a linear equation in the form [tex]\( y = mx + b \)[/tex] is represented by [tex]\( m \)[/tex].
Let's identify the slopes for each equation:
- For equation A: [tex]\( y = 10x - 5 \)[/tex]
- The slope [tex]\( m \)[/tex] is [tex]\( 10 \)[/tex].
- For equation B: [tex]\( y = -14x + 1 \)[/tex]
- The slope [tex]\( m \)[/tex] is [tex]\( -14 \)[/tex].
- For equation C: [tex]\( y = \frac{3}{4}x - 9 \)[/tex]
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{3}{4} \)[/tex].
- For equation D: [tex]\( y = 2x + 8 \)[/tex]
- The slope [tex]\( m \)[/tex] is [tex]\( 2 \)[/tex].
To determine which graph is the steepest, we need to find the slope with the largest absolute value, as the absolute value represents the steepness regardless of the direction (positive or negative).
Compare the absolute values of the slopes:
- [tex]\( |10| = 10 \)[/tex]
- [tex]\( |-14| = 14 \)[/tex]
- [tex]\( \left|\frac{3}{4}\right| = 0.75 \)[/tex]
- [tex]\( |2| = 2 \)[/tex]
The largest absolute value among these is [tex]\( 14 \)[/tex], which corresponds to the slope of equation B.
Thus, the equation with the steepest graph is:
B. [tex]\( y = -14x + 1 \)[/tex]
