Question

5x-3y=-6

find the x-intercept and y-intercept

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the x-intercept, set y=0 in the equation and solve for x:

5x - 3(0) = -6
5x = -6
x = -6/5

Therefore, the x-intercept is (-6/5, 0).

To find the y-intercept, set x=0 in the equation and solve for y:

5(0) - 3y = -6
-3y = -6
y = -6/-3
y = 2

Therefore, the y-intercept is (0, 2).

Answer 2

4x-4y=0

find the x and y intercepts

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the x-intercept, set y=0 in the equation and solve for x:

4x - 4(0) = 0
4x = 0
x = 0

Therefore, the x-intercept is (0, 0).

To find the y-intercept, set x=0 in the equation and solve for y:

4(0) - 4y = 0
-4y = 0
y = 0

Therefore, the y-intercept is (0, 0).

Answer 4

find the slope of the line that passes through the points (2,-6) and (4,-12)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the slope of a line passing through two points, we use the formula:

Slope = (y2 - y1) / (x2 - x1)

Let's substitute the given values into the formula:

(x1, y1) = (2, -6)
(x2, y2) = (4, -12)

Slope = (-12 - (-6)) / (4 - 2)
Slope = (-12 + 6) / (4 - 2)
Slope = -6 / 2

Simplifying the fraction, we get:
Slope = -3

Therefore, the slope of the line passing through the points (2,-6) and (4,-12) is -3.

Answer 6

find slope of the line that passes through the points

(2,-1) and (-9,3)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the slope of a line passing through two points, we use the formula:

Slope = (y2 - y1) / (x2 - x1)

Let's substitute the given values into the formula:

(x1, y1) = (2, -1)
(x2, y2) = (-9, 3)

Slope = (3 - (-1)) / (-9 - 2)
Slope = (3 + 1) / (-9 - 2)
Slope = 4 / (-11)

Therefore, the slope of the line passing through the points (2, -1) and (-9, 3) is -4/11.

Answer 8

find the slope of a line passing through the points

(6,5) and (6,8)
(3,10) and (-7,10)

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:

Slope = (y2 - y1) / (x2 - x1)

For the first set of points (6, 5) and (6, 8):
Slope = (8 - 5) / (6 - 6)
Slope = 3 / 0

Since the denominator is 0, the slope is undefined.

For the second set of points (3, 10) and (-7, 10):
Slope = (10 - 10) / (-7 - 3)
Slope = 0 / -10
Slope = 0

Therefore, the slope of the line passing through the points
(6, 5) and (6, 8) is undefined, and the slope of the line passing through the points (3, 10) and (-7, 10) is 0.

Answer 10

(a8)(a2)(a4)

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the product of these three terms, you can combine the exponents:

(a^8) * (a^2) * (a^4) = a^(8+2+4) = a^14

Therefore, the product is a^14.

Answer 12

product rule to simplify, write result using exponents

(a8) * (a2) * (a4)

Answer 13

[AI-generated answer — Bot GPT 3.5]

To simplify the expression using the product rule and write the result using exponents, we can add the exponents of the same base, which in this case is 'a'.

(a^8) * (a^2) * (a^4) = a^(8 + 2 + 4) = a^14

Therefore, the simplified expression is a^14.

Answer 14

simplify expression, write the result using positive exponents only

(-3)^-4

Answer 15

[AI-generated answer — Bot GPT 3.5]

To simplify the expression and write the result using positive exponents only, we can use the rule that states when a negative exponent is raised to, it becomes the reciprocal of the positive exponent.

(-3)^-4 = 1 / (-3)^4

Now, we can evaluate (-3)^4:

(-3)^4 = (-3) * (-3) * (-3) * (-3) = 81

Therefore, the simplified expression is 1 / 81.

Answer 16

simplify expression, write the result using positive exponents only

(-3)-4

Answer 17

[AI-generated answer — Bot GPT 3.5]

To simplify (-3)^-4 and write the result using positive exponents only, we can use the rule that states when a negative exponent is applied to a number, it becomes the reciprocal of that number raised to the positive exponent.

(-3)^-4 = 1 / (-3)^4

Now, we can evaluate (-3)^4:

(-3)^4 = (-3) * (-3) * (-3) * (-3) = 81

Therefore, the simplified expression is 1 / 81.