Question

Bruno is a manager at a factory that makes in-line skates. The equation 200x - y + 500 = 0 relates y, the number of pairs of skates the factory has in the warehouse, and x, the number of hours after Bruno starts his shift. Show that the equation is a linear equation by writing it in slope-intercept form. Show your work.

a) y = 200x + 500
b) y = 200x - 500
c) y = -200x + 500
d) y = -200x - 500

Answer 1

The equation 200x - y + 500 = 0 can be written in slope-intercept form as y = 200x + 500, which indicates that it is a linear equation with a slope of 200 and a y-intercept of 500.

Step-by-step explanation:

To show that the equation 200x - y + 500 = 0 is linear and to write it in slope-intercept form, we need to solve the equation for y. The goal is to get y alone on one side of the equal sign and express everything else in terms of x. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Here are the steps to rearrange the equation:

1. Start with the given equation: 200x - y + 500 = 0.
2. Add y to both sides to get it alone on one side: 200x + 500 = y.
3. Rearrange the equation to match the slope-intercept form: y = 200x + 500.

Now the equation is in the slope-intercept form. The slope (m) is 200, representing the rate at which the number of pairs of skates changes each hour, and the y-intercept (b) is 500, the number of pairs of skates in the warehouse at the start of Bruno's shift.