Question

the graph shows the relationship between the number of hours maria spends reading (x) and the total number of pages she reads (y). the line passes through the point (4, 120).
marias reading time
which equation shows the relationship?
○ $y = 40x$
○ $y = 30x$
○ $y = 25x$
○ $y = 50x$

Explanation:

Step1: Recall the slope-intercept form

The graph is a straight line passing through the origin, so its equation is of the form \( y = mx \), where \( m \) is the slope (rate of change).

Step2: Calculate the slope using the point (4, 120)

The slope \( m \) is calculated as \( \frac{y}{x} \) for a point \( (x, y) \) on the line. Substituting \( x = 4 \) and \( y = 120 \), we get \( m=\frac{120}{4}=30 \).

Step3: Determine the equation

Since \( m = 30 \), the equation of the line is \( y = 30x \). We can also verify by plugging \( x = 4 \) into each option:

• For \( y = 40x \), \( y = 40\times4 = 160

eq120 \).

• For \( y = 30x \), \( y = 30\times4 = 120 \) (matches the point).
• For \( y = 25x \), \( y = 25\times4 = 100

eq120 \).

• For \( y = 50x \), \( y = 50\times4 = 200

eq120 \).

Answer:

\( y = 30x \) (the option with \( y = 30x \))