Question

If the demand for video games is 250 units when the price is $50 and the demand is 25 units when the price is $125, write the equation which gives y as a linear function of x. Put the equation in slope-intercept form.

a) y = -2.5x + 375
b) y = 2.5x - 125
c) y = -125x + 375
d) y = 375x - 125

Answer 1

The equation which gives y as a linear function of x is y = -3x + 400 in slope-intercept form.

Step-by-step explanation:

To write the equation which gives y as a linear function of x, we need to find the slope and the y-intercept. The slope can be calculated using the formula: slope = (change in y) / (change in x). In this case, the change in y is 25 - 250 = -225 and the change in x is 125 - 50 = 75. So, the slope is -225 / 75 = -3.

Using the point-slope form of a linear equation, we can write: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Let's use the point (50, 250):

y - 250 = -3(x - 50)

To put the equation in slope-intercept form, we need to isolate y:

y = -3x + 150 + 250

y = -3x + 400

The equation which gives y as a linear function of x in slope-intercept form is y = -3x + 400.