Question

1. sandy wears contact lenses. she starts the year with 5 pairs of lenses, and she uses 3 pairs of contacts every 2 months. write an equation in standard form to represent sandy’s supply of contact lenses, y, after x months.

Explanation:

Step1: Determine the rate of use

First, find the rate at which Sandy uses contact lenses. She uses 3 pairs every 2 months, so the rate \( r \) is \( \frac{3}{2} \) pairs per month.

Step2: Identify the initial amount

The initial number of pairs of lenses, \( b \), is 5.

Step3: Write the slope - intercept form

The slope - intercept form of a linear equation is \( y=mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value). Here, \( m=\frac{3}{2} \) and \( b = 5 \), so the equation is \( y=\frac{3}{2}x+5 \).

Step4: Convert to standard form

The standard form of a linear equation is \( Ax + By=C \), where \( A \), \( B \), and \( C \) are integers and \( A\geq0 \).
Start with \( y=\frac{3}{2}x + 5 \).
Subtract \( \frac{3}{2}x \) from both sides: \( -\frac{3}{2}x+y=5 \).
Multiply every term by - 2 to make the coefficient of \( x \) a positive integer: \( 3x-2y=- 10 \).

Answer:

\( 3x - 2y=-10 \)