Question

The given graph shows the earnings of manager A.The earnings of manager B is given by the equation $y=15x+50,$ where $x$ represents the working time (hr) and $y$ represents the amount of money $\left(\$\right).$


If the bonus amount received by them is represented by the y-intercept for each, then choose the correct statement.

• A. Manager A received more bonus than manager B.
• B. Neither of them have received any bonus amount.
• C. Manager B received more bonus than manager A.
• D. Both managers received a bonus of $\$30.$

Answer 1

The correct option is C Manager B received more bonus than manager A.

Finding bonus amount of manager A:
y-intercept: It is the point where the graph of the line touches or crosses the y-axis. The x-coordinate is zero at this point.
The graph of manager A touches the y-axis at $(0,30)$:
$\Rightarrow$ y-intercept $=30$
The bonus amount of manager $A=\$30$
Finding the bonus amount of manager B:
For the equation of the straight line, $y=mx+b:$
y-intercept $=b$
Comparing the equation of the straight line $y=15x+50$ with $y=mx+b,$ we get:
y-intercept $=b=50$
The bonus amount of manager $B=\$50$
Manager B received more bonus than manager A.
$\to$ Option B is correct.