Question

does y vary directly with x?

8 13
16 26
24 39

Answer 1

[AI-generated answer — Bot GPT 3.5]

Yes, y varies directly with x in this case. This can be determined by comparing the ratios of y to x for each set of values.

For the first set of values (8, 13), the ratio of y to x is 13/8 = 1.625.
For the second set of values (16, 26), the ratio of y to x is 26/16 = 1.625.
For the third set of values (24, 39), the ratio of y to x is 39/24 = 1.625.

Since the ratios of y to x are constant and equal in all three sets, we can conclude that y varies directly with x.

Answer 2

does y vary directly with x

40 32
28 16
16 12

Answer 3

[AI-generated answer — Bot GPT 3.5]

No, y does not vary directly with x in this case. To determine if y varies directly with x, we need to compare the ratios of y to x for each set of values.

For the first set of values (40, 32), the ratio of y to x is 32/40 = 0.8.
For the second set of values (28, 16), the ratio of y to x is 16/28 = 0.571.
For the third set of values (16, 12), the ratio of y to x is 12/16 = 0.75.

Since the ratios of y to x are not constant and differ in the three sets, we can conclude that y does not vary directly with x.

Answer 4

write an equation i point slope form for the line through the given point with the given slope

(8, 3); m = 6

Answer 5

[AI-generated answer — Bot GPT 3.5]

The equation of the line in point-slope form is:

y - y₁ = m(x - x₁)

Substituting the given values:

y - 3 = 6(x - 8)

Answer 6

write an equation i point slope form for the line through the given point with the given slope

(-10, -6); m = -5/8

Answer 7

[AI-generated answer — Bot GPT 3.5]

The equation of the line in point-slope form is:

y - y₁ = m(x - x₁)

Substituting the given values:

y - (-6) = (-5/8)(x - (-10))

Answer 8

write an equation for the line parallel to y = 3x + 7; (2, 10)

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find a line parallel to y = 3x + 7, we can use the same slope but a different y-intercept.

The slope of y = 3x + 7 is 3.

Using the formula y - y₁ = m(x - x₁) with the point (2, 10), we have:

y - 10 = 3(x - 2)

Expanding gives:

y - 10 = 3x - 6

Rearranging the equation to slope-intercept form gives:

y = 3x + 4

So, the equation for the line parallel to y = 3x + 7 passing through the point (2, 10) is y = 3x + 4.

Answer 10

write an equation for a line perpendicular to y - 3 = 8/3(x + 2); (-2, 3)

Answer 11

[AI-generated answer — Bot GPT 3.5]

First, let's rewrite the given equation in slope-intercept form (y = mx + b):

y - 3 = 8/3(x + 2)

Distributing and rearranging the equation:

y - 3 = (8/3)x + 16/3

y = (8/3)x + 16/3 + 3

y = (8/3)x + 16/3 + 9/3

y = (8/3)x + 25/3

The slope of the given line is 8/3. The slope of a line perpendicular to this line will be the negative reciprocal of 8/3, which is -3/8.

Now using the point (-2, 3), we can substitute into the point-slope form equation (y - y₁ = m(x - x₁)):

y - 3 = (-3/8)(x - (-2))

Simplifying:

y - 3 = (-3/8)(x + 2)

Multiplying through by 8 to eliminate the fraction:

8(y - 3) = -3(x + 2)

8y - 24 = -3x - 6

3x + 8y = -18