Question

Can you help me please

Answer 1

No, the slope's are not the same

Short-cut explanation:

Simply count the spaces between the two lines at the very top then compare to the number of space between at the very bottom of the graph.

There are 2 spaces between the two lines at the top. There seems to be 1 and 1/2 spaces at the very bottom.

`2\\eq 1.5` , therefore, not parallel.

If they are the same, then it is parallel. Although, in this case, it is not(Shown on the graph).

Answer 2

Basic Concept:

A criterion for parallel lines is that they should have equal slopes. If the slopes of these lines is equal, these lines are parallel and are intersecting if the slopes are not equal

let the line on the left be 'line 1' and the line on the right be 'line 2'

Slope of Line 1:

We are given 2 points on the line and we will use them to get its slope

We know that the slope of a line is the change in its y-ordinate divided by its change in x - ordinate

The points given are: (-3 , -5) and (0 , 4)

Change in x:

The change in x of these 2 coordinates can be calculated by subtracting their x- ordinates

Change in x (Δx) = x1 - x2

Δx = -3 - 0

Δx = -3

Change in y:

The change in y of these 2 can similarly be calculated by subtrating the y-ordinates

change in y (Δy) = y1 - y2

Δy = -5 - 4

Δy = -9

Slope of the line:

Since the slope = Δy / Δx

Replacing the known values:

Slope = -9 / -3

Slope = 3

Therefore, the slope of 'line 1' is 3

Slope of Line 2:

We are given 2 points on the line and we will use them to get its slope

We know that the slope of a line is the change in its y-ordinate divided by its change in x - ordinate

The points given are: (0 , -6) and (4 , 4)

Change in x:

The change in x of these 2 coordinates can be calculated by subtracting their x- ordinates

Change in x (Δx) = x1 - x2

Δx = 0 - (4)

Δx = -4

Change in y:

The change in y of these 2 can similarly be calculated by subtrating the y-ordinates

change in y (Δy) = y1 - y2

Δy = -6 - 4

Δy = -10

Slope of the line:

Since the slope = Δy / Δx

Replacing the known values:

Slope = -10 / -4

Slope = 5/2

Therefore, the slope of 'line 2' is 5/2

Conclusion:

We have calculated the slope of both the lines.

now, we will compare the slopes to find out if the lines are parallel or not

Slope 1 = 3

Slope 2 = 5/2

Since the slopes are NOT equal, the lines are not parallel