A public pool charges a membership fee and a fee for each visit. The equation \(\text{y} = 3\text{x} + 50\) represents the cost y for x visits.

a. After locating the y-intercept on the coordinate plane shown, can you move up three gridlines and right one gridline to find a second point? Explain.

b. Graph the equation \(\text{y} = 3\text{x} + 50\). Include axis labels. Then interpret the slope and y-intercept.

c. How many visits to the pool can a member get for $200?

Explain the Error

A student says that the slope of the line for the equation \(\text{y} = 20 - 15\text{x}\) is 20 and the y-intercept is 15. Find and correct the error.

Critical Thinking

Suppose you know the slope of a linear relationship and a point that its graph passes through. Can you graph the line even if the point provided does not represent the y-intercept? Explain.

Make a Conjecture

Graph the lines \(\text{y} = 3\text{x}\), \(\text{y} = 3\text{x} - 3\), and \(\text{y} = 3\text{x} + 3\). What do you notice about the lines? Make a conjecture based on your observation.