A1-U2.3 Lesson Check: Solving Problems w/ Standard Form

• 2

• 3

• 6

• 0

Answer explanation

To find the y-intercept, set x = 0 in the equation 2x + 3y = 6. This gives 3y = 6, so y = 2. Therefore, the y-intercept is 2.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Answer explanation

To find the slope from the equation 4x - 5y = 20, use Ax + By = C, and divide the opposite of A by B. So -4/-5 or 4/5.

Tags

CCSS.HSA.REI.D.10

CCSS.HSS.ID.C.7

A company sells notebooks for $5 each and pens for $2 each. If the total sales amount to $50, which equation represents this situation?

Answer explanation

The equation 5x + 2y = 50 represents the total sales, where x is the number of notebooks sold at $5 each and y is the number of pens sold at $2 each. This correctly sums to the total sales of $50.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

• 3

• 4

• 12

• 0

Answer explanation

To find the x-intercept, set y = 0 in the equation 3x + 4y = 12. This gives 3x = 12, so x = 4. Therefore, the x-intercept is 4.

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Answer explanation

The perimeter of a rectangle is given by the formula 2l + 2w. Since the perimeter is 24 units, the correct equation is 2l + 2w = 24, which matches the first answer choice.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

• 1

• -1

• 2

• -0.5

Answer explanation

To find the slope of the line from the equation x + 2y = 8, rearrange it to slope-intercept form (y = mx + b). This gives 2y = -x + 8, or y = -0.5x + 4. The slope (m) is -0.5.

Tags

CCSS.HSG.GPE.B.5

CCSS.HSS.ID.C.7

A store sells apples for $3 each and bananas for $1 each. If a customer buys a total of 10 fruits for $20, which equation represents this situation?

Answer explanation

Let x be the number of apples and y be the number of bananas. The total number of fruits is x + y = 10, and the total cost is 3x + y = 20. Thus, the correct equation representing the situation is 3x + y = 20.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

• 5

• -5

• 3

• -3

Answer explanation

To find the y-intercept, set x = 0 in the equation 5x - 3y = 15. This gives -3y = 15, so y = -5. Thus, the y-intercept is -5.

Tags

CCSS.HSA.REI.D.10

CCSS.HSS.ID.C.7

A bakery sells cakes for $15 each and cookies for $3 each. If the total sales amount to $90, which equation represents this situation?

Answer explanation

The equation 15x + 3y = 90 represents the total sales, where x is the number of cakes sold at $15 each and y is the number of cookies sold at $3 each. This correctly sums to the total sales of $90.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

Answer explanation

To find the slope from the equation 7x - 2y = 14, rearrange it to slope-intercept form (y = mx + b). This gives y = 7x/2 -7.

Tags

CCSS.HSS.ID.C.7