Question

Compare the line passing through the points (-2,-9) and (4, 6) with the line given by the equation

y = 2/5x -4.

A) they have the same slope

B) they have the same x-intercept

C) the two lines are perpendicular

D) they have the same Y-intercept

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points:

`(x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)`

We can find the slope:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}`

Thus, the equation is of the form:

`y = \frac {5} {2} x + b`

We substitute one of the points and find "b":

`6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4`

Finally, the equation is:

`y = \frac {5} {2} x-4`

Thus, it is observed that the lines have the same y-intercept

Answer:

Option D