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 sam
Mathematics
mia5944
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 xintercept
C) the two lines are perpendicular
D) they have the same Yintercept
y = 2/5x 4.
A) they have the same slope
B) they have the same xintercept
C) the two lines are perpendicular
D) they have the same Yintercept
1 Answer

1. User Answers carlosego
For this case we have that by definition, the equation of a line in the slopeintersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cutoff point with the y axis
We have the following points:
[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): ( 2, 9)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} y_ {1}} {x_ {2} x_ {1}} = \frac {96} { 24} = \frac {15} { 6} = \frac {5} {2}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {5} {2} x + b[/tex]
We substitute one of the points and find "b":
[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\610 = b\\b = 4[/tex]
Finally, the equation is:
[tex]y = \frac {5} {2} x4[/tex]
Thus, it is observed that the lines have the same yintercept
Answer:
Option D