Question

For question 1, find the x- and y-intercept of the line.

-10x+5y = 40

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the x-intercept, we set y equal to zero and solve for x:

-10x + 5(0) = 40
-10x = 40
Dividing both sides by -10, we get:
x = -4
So the x-intercept is (-4, 0).

To find the y-intercept, we set x equal to zero and solve for y:
-10(0) + 5y = 40
5y = 40
Dividing both sides by 5, we get:
y = 8
So the y-intercept is (0, 8).

Answer 2

5x + 4y = 80

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the x-intercept, we set y equal to zero and solve for x:

5x + 4(0) = 80
5x = 80
Dividing both sides by 5, we get:
x = 16
So the x-intercept is (16, 0).

To find the y-intercept, we set x equal to zero and solve for y:
5(0) + 4y = 80
4y = 80
Dividing both sides by 4, we get:
y = 20
So the y-intercept is (0, 20).

Answer 4

Write y=1/6x+4 in standard form using integers.

Answer 5

[AI-generated answer — Bot GPT 3.5]

To write the equation y = (1/6)x + 4 in standard form using integers, we can start by multiplying the entire equation by 6 to eliminate the fraction:

6y = x + 24

Next, we rearrange the equation so that the x and y terms are on the same side and the constant term is on the other side:

-x + 6y = 24

Finally, we multiply through by -1 to make the x coefficient positive:

x - 6y = -24

Therefore, the standard form of the equation is x - 6y = -24.

Answer 6

The grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $22.

Answer 7

[AI-generated answer — Bot GPT 3.5]

Let k represent the weight of kumquats in pounds, and let p represent the weight of Asian pears in pounds.

Since the kumquats are sold for $4.75 per pound and the Asian pears are sold for $2.25 per pound, we can write the following equation:

4.75k + 2.25p = 22

Now, to convert this equation into standard form using integers, we can multiply through by 100 to remove the decimals:

475k + 225p = 2200

Therefore, the equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $22 is 475k + 225p = 2200.