Question

this graph shows a linear relationship between the number of comic books pilar buys at the store, x, and the amount of money, in dollars, she has afterwards, y.

(a) write an equation for this line.

(b) if pilar buys 3 comic books, how much money will she have left?

Explanation:

Part (a)

Step 1: Identify the slope and y-intercept

The linear equation is in the form \( y = mx + b \), where \( b \) is the y-intercept and \( m \) is the slope. From the graph, when \( x = 0 \), \( y = 20 \), so the y-intercept \( b = 20 \). To find the slope, we use two points, e.g., \( (0, 20) \) and \( (5, 0) \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 20}{5 - 0}=\frac{-20}{5}=-4 \).

Step 2: Write the equation

Substitute \( m = - 4 \) and \( b = 20 \) into \( y = mx + b \). So the equation is \( y=-4x + 20 \).

Step 1: Substitute \( x = 3 \) into the equation

We use the equation from part (a), \( y=-4x + 20 \). Substitute \( x = 3 \) into it: \( y=-4(3)+20 \).

Step 2: Calculate the value

First, calculate \( -4\times3=-12 \), then \( y=-12 + 20 = 8 \).

Answer:

\( y=-4x + 20 \)

Part (b)