Question

nate starts with 5 dollars in his account. he earns 10 dollars per hour mowing lawns and deposits the earnings into his account. tamia starts with -15 dollars in her account. she earns 10 dollars per hour mowing lawns and deposits the earnings into her account. what are the slopes of each of the lines? nate: ( d = 5 + 10x ) the slope of nate’s line is d. tamia: ( d = -15 + 10x ) the slope of tamia’s line is .

Explanation:

Step1: Recall Slope-Intercept Form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For a linear equation in the form \(d=mx + b\) (where \(d\) is the amount of money in the account and \(x\) is the number of hours), the coefficient of \(x\) is the slope.

Step2: Analyze Nate's Equation

Nate's equation is \(d = 5+10x\). Comparing with \(d=mx + b\), the coefficient of \(x\) (which is \(m\)) is 10. So the slope of Nate's line is 10.

Step3: Analyze Tamia's Equation

Tamia's equation is \(d=- 15 + 10x\) (or \(d = 10x-15\)). Comparing with \(d=mx + b\), the coefficient of \(x\) (which is \(m\)) is 10. So the slope of Tamia's line is 10.

Answer:

The slope of Nate's line is 10. The slope of Tamia's line is 10.