Greetings!
To find that these two slopes are the same, you can calculate the gradients of the two lines, which is what all the options are.
The equation for the gradient is:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
Where the differeny y and x values are the two co-ordinates of the lines starting and end point.
Take the line JL, one of the two sets of coordinates are (-4 , 0) and the other set is (-7, 4)
If you use these two sets to substitute into the equation for the gradient, you can use either y coordinates in both sets as y1 or y2 as long as this method is throughout and the x value is the same in both sets ( both numbers are x1 and y1, one cannot be x1 and the other y2).
Lets use ( -4 , 0) and (-7 , 4) which are the coordinates for JL.
y1 = 4 and y2 = 0
0 - 4
Now lets use the two x values:
x1 = -7 and x2 = -4
(-4) - (-7)
Simply put these two equations in a fraction:
[tex]\frac{0 - 4}{-5 - (-7)}[/tex]
Now choose another two sets of values for MP, such as (-10 , 8) and (-1 , -4)
y1 = 8 and y2 = -4
-4 - 8
Lets use the two x values:
x1 = -10 and x2 = -1
-1 - (-10)
Put them into a fraction:
[tex]\frac{-4 - 8}{-1 - (-10)}[/tex]
Now these two fractions can be put together, putting an equal sign in middle because they both are same gradient:
[tex]\frac{0 - 4}{-5 - (-7)} = \frac{-4 - 8}{-1 - (-10)}[/tex]
Meaning that your answer if G!
Hope this helps!
