4C: Initial Value (y-Intercept)

True or false:

The y-intercept of a function ALWAYS occurs where y is equal to zero.

• True

• False

Answer explanation

y-intercept is where x is equal to zero: x must have a value of zero in order for a point to be on the y-axis.

Which ordered pair could represent the y-intercept of a function.

• (0, 4)

• (4, 4)

• (4, 0)

• None of these.

Answer explanation

Any point where x has a value of 0 will rest somewhere on the y-axis.

What is the y-intercept of this graph?

• (0,1)

• (0,-2)

• (0,0)

• (0,3)

Answer explanation

(0,1) is the point on the graphed line that rests on the y-axis (intersects the y-axis)

_{What is the y-intercept of the line?}

• (0, 1/2)

• (0,1)

• (0, -1/2)

• (0,-1)

Answer explanation

(0,-1) is the point on the graphed line that rests on the y-axis (intersects the y-axis)

What is the y-intercept?

• (0,7)

• (0,0)

• (0,1)

• (0,2)

Answer explanation

(0,7) is the point in the table where x has a value of zero, which means this point rests on the y-axis (intersects the y-axis)

Determine the y-intercept of the table

• (0,-2)

• (0,2)

• (0,5)

• (0,-4)

Answer explanation

Like we did in toothpick patterns and stacking cups: use your rate of change to determine the value of y when x is zero.

Given the list of ordered pairs, what is the x-intercept?

(8,10), (3, -4), (0, 8), (4, -3), (9, 0)

• (8,10)

• 8, 3, 0, 4, 9

• (0,8)

• (9,0)

Answer explanation

Look for the point where x has a value of zero, so you know the point rests on the y-axis.

What is the y intercept?

y = 2x - 3

• 3

• -3

• 1

• 2

Answer explanation

If we substitute 0 in for x, we can solve for y to see what the y-intercept is. (Find the point where x=0)

What is the y-intercept in the equation y= -2x + 5

• -2

• 3

• 5

• Cannot be Determined

Answer explanation

If we substitute 0 in for x, we can solve for y to see what the y-intercept is. (Find the point where x=0)

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. What is the initial value in this scenario?

• $15

• $2

• Not enough information is given

Answer explanation

The initial value is a value present in the scenario that isn't part of the rate involved (often times some initial/starting value).

EXAMPLE: base of the cup in stacking cups, toothpick we built off of in toothpick patterns.