A 2-pound box of salt sells for $0.89, and a 5-pound box sells for $2.09. What is the linear equation for this?

y = ax + b;
0.89 = a * 2 + b and 2.09 = a * 5 + b => => 2.09 - 0.89 = a * 5 + a * 2 + b - b => 1.20 = 3 * a => a = 1.20 / 3 => a = 0.40; b = 0.89 - 0.40 * 2 => b = 0.89 - 0.80 => b = 0.09;
y = 0.40x + 0.09 => 0.40x - y + 0.09 = 0 is the linear equation.

Answered by crisforp | 2024-06-10

The linear equation that relates the weight of salt to its price is y = 0.40 x + 0.09 , where x is the weight in pounds and y is the price in dollars. The slope a = 0.40 indicates the price per pound, while b = 0.09 is the y-intercept, representing a starting price value. The equation can also be expressed in standard form as 0.40 x − y + 0.09 = 0 .
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Answered by crisforp | 2024-12-26