Question

part #2: write the equation of the line and explain its meaning.

find the slope:
slope =

find the y - intercept:
y - int =

write the equation and explain its meaning in detail:

what is the distance in 5 hours?
answer =

find the slope:
slope =

find the y - intercept:
y - int =

write the equation and explain its meaning in detail:

what is the grade if the student completes 24 assignments?
answer =

Explanation:

Travel Distance

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0,360)\) and \((6,0)\), \(m=\frac{0 - 360}{6-0}=\frac{- 360}{6}=-60\)

Step2: Determine the y - intercept

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,360)\), \(y - int=360\)

Step3: Write the equation

The equation of a line is \(y=mx + b\), so \(y=-60x + 360\). The slope \(-60\) means the distance decreases by 60 miles per hour. The y - intercept 360 means the initial distance (at \(x = 0\) hours) is 360 miles.

Step4: Find the distance at \(x = 5\)

Substitute \(x = 5\) into \(y=-60x + 360\), \(y=-60\times5+360=-300 + 360 = 60\)

Math Homework

Step1: Calculate the slope

Using the points \((10,85)\) and \((20,95)\), \(m=\frac{95 - 85}{20 - 10}=\frac{10}{10}=1\)

Step2: Determine the y - intercept

Use the point - slope form \(y - y_1=m(x - x_1)\). Using \((x_1,y_1)=(10,85)\) and \(m = 1\), \(y-85=1\times(x - 10)\), \(y=x+75\). So \(y - int = 75\)

Step3: Write the equation

The equation is \(y=x + 75\). The slope \(1\) means that for each additional completed assignment, the grade increases by 1 percentage point. The y - intercept 75 means that if \(x = 0\) (no assignments completed), the grade is 75%.

Step4: Find the grade at \(x = 24\)

Substitute \(x = 24\) into \(y=x + 75\), \(y=24+75=99\)

Answer:

• Travel Distance:
• SLOPE=\(-60\)
• Y - Int=\(360\)
• Equation: \(y=-60x + 360\), meaning distance decreases 60 miles per hour from an initial 360 miles
• ANSWER=\(60\) miles
• Math Homework:
• SLOPE=\(1\)
• Y - Int=\(75\)
• Equation: \(y=x + 75\), meaning grade increases 1% per assignment with an initial 75%
• ANSWER=\(99\) percent