Question

PLEASE HELP ME, What is the equation of the line in slope-intercept form?

Responses


y=−3/5x+1

y equals negative fraction 3 over 5 end fraction x plus 1


y=−3/5x+15

y equals negative fraction 3 over 5 end fraction x plus 1 fifth


y=−5/3x−3

y equals negative fraction 5 over 3 end fraction x minus 3


y=−3/5x

Answer 1

Explanation:

The correct equation is **y = -3/5x + 1**.

The other equations are incorrect because they do not have the correct slope. The slope of the line that reflects ABCD onto itself is -3/5. This means that for every 3 units that we move to the left, we need to move 5 units up.

The equation y = -3/5x + 1 satisfies this condition. If we move 3 units to the left, the y-coordinate will increase by 5. This is exactly what we need to do to reflect the points of square ABCD onto themselves.

The other equations do not have this property. For example, the equation y = -3/5x + 15 would cause the points of square ABCD to be reflected onto themselves, but it would also stretch the square vertically. This is because the y-coordinate is increasing by 15 for every 3 units that we move to the left.

The equation y = -5/3x - 3 would cause the points of square ABCD to be reflected onto themselves, but it would also stretch the square horizontally. This is because the x-coordinate is decreasing by 3 for every 5 units that we move up.

The equation y = -3/5x is the only equation that correctly reflects the points of square ABCD onto themselves without stretching or shrinking the square.

Answer 2

y = −3/5x + 1/5

Explanation:

In order to find the slope-intercept form of a line given the coordinates of two points on the line, we have to first calculate its slope using the following formula:

`\boxed{m = (y_2 - y_1)/(x_2 - x_1)}`,

where:

m ⇒ slope

(x₁, y₁), (x₂, y₂) ⇒ coordinates of the two points (-3, 2), (2, -1)

Using the above formula:

`m = (2 - (-1))/(-3-2)`

⇒
`m = \bf -(3)/(5)`

Next, we have to use the following formula to find the slope-intercept form of the line:

`\boxed{y-y_1 = m(x-x_1)}`

where:

m ⇒ slope

(x₁, y₁) ⇒ coordinates of any point on the line

Using the coordinates (-3, 2):

`y - 2 = -(3)/(5) (x-(-3))`

⇒
`y -2= -(3)/(5) (x+3)`

⇒
`y-2 = -(3)/(5)x -(9)/(5)` [Distributing the fraction into the brackets]

⇒
`y = -(3)/(5)x - (9)/(5) + 2` [Adding 2 to both sides of the equation]

⇒
`y = -(3)/(5)x + (1)/(5)`

Therefore, the second answer choice is the correct one.