Applications of X and Y Intercepts

Discuss the graphical representation of x-intercepts and y-intercepts of a function.

• Locate the points where the graph intersects the x-axis and y-axis

• Measure the distance between the x-intercept and y-intercept

• Find the slope of the graph at the x-intercept and y-intercept

• Count the number of lines intersecting the x-axis and y-axis

Explain the concept of intercepts in the context of functions and their applications in real-life scenarios.

• Intercepts are the points where a function reaches its maximum value (max-intercept) or minimum value (min-intercept).

• In real-life scenarios, intercepts have no practical applications and are purely theoretical concepts.

• Intercepts are the points where a function crosses the z-axis (z-intercept) or the w-axis (w-intercept).

• Intercepts are the points where a function crosses the x-axis (x-intercept) or the y-axis (y-intercept). In real-life scenarios, intercepts can represent important values such as the break-even point in business or the time and distance at which two objects intersect in physics.

What are the similarities and differences between x-intercepts and y-intercepts of functions?

• x-intercepts occur when the graph is increasing and y-intercepts occur when the graph is decreasing

• x-intercepts occur when y=0 and y-intercepts occur when x=0

• x-intercepts occur when x=0 and y-intercepts occur when y=0

• Both intercepts are points where the graph crosses an axis, but x-intercepts occur when y=0 and y-intercepts occur when x=0.

What are the green dots called?

• y-intercepts

• maximum

• minimum

• zeros/x-intercepts

• A

• B

• C

• D

• A

• B

• C

• D

What are the x and y intercepts of the graph?

• x intercept: 4, y intercept 3

• x intercept: 3, y intercept 4

• x intercept: 4, y intercept -3

• x intercept: -4, y intercept 3

What is the x and y intercept for the following equation ?

4x - 10y = 20

*SHOW WORK*

• x - int = (4, 0)

  y-int = (0, -10)

• x-int = (5, 0)

  y-int = (0, 2)

• x - int = (5, 0)

  y int = (0, -2)

• x -int = (-4, 0)

  y -int = (0, -10)

What is the y-intercept of this line?

• -3

• -2

• 0

Shawn recently went skydiving for his birthday. The relationship between the time in seconds, x, and his elevation in feet, y, is shown in the table below. Find the y-intercept and explain its meaning.

• 12,500; Shawn ascends at a rate of 12,500 feet per second.

• -175; Shawn descends at a rate of 175 feet per second.

• -175; Shawn's initial height is -175 feet.

• 12,500; Shawn's initial height is 12,500 feet.