Pencils cost 20 cents and pens cost 50 cents. Mabel buys x pencils and y pens, spending $2.00.
what is the slope and what does it represent?
what is the y-intercept and what does it represent?
To find the slope and y-intercept, we need to understand the given information in terms of a linear equation.
Let's represent the number of pencils as "x" and the number of pens as "y".
We know that pencils cost 20 cents each and pens cost 50 cents each, and Mabel spent $2.00 in total. From this information, we can write the equation:
0.20*x + 0.50*y = 2.00
Now, we need to rearrange the equation into the standard form y = mx + b, where m represents the slope and b represents the y-intercept.
0.50*y = -0.20*x + 2.00
Dividing both sides of the equation by 0.50:
y = (-0.20/0.50)*x + (2.00/0.50)
Simplifying further:
y = -0.40*x + 4.00
Now we can identify the slope and y-intercept.
1. Slope (m): The coefficient of x (-0.40 in this case) represents the slope of the line. The slope indicates the change in y for every unit change in x. In this scenario, the slope of -0.40 means that for every additional pencil Mabel buys (1 unit increase in x), the number of pens she buys decreases by 0.40 (0.40 units decrease in y).
2. Y-intercept (b): The constant term (4.00 in this case) represents the y-intercept. The y-intercept is the point on the y-axis where the line intersects. In this context, it represents the number of pens Mabel would buy if she didn't buy any pencils. So, the y-intercept of 4.00 means that Mabel would buy 4 pens if she didn't buy any pencils.