Which is an equation of the line that passed through ( 2,-5 ) and ( 6,3 ).
A. Y= 1/2X - 6
B. Y= 1/2X
C. Y= 2X + 12
D. Y= 2X - 9
I really need help with this question so can anyone please explain to me how I can solve this question and please explain to me how you found the answer to this question step by step.
Look up the two-point form of the equation for a line. It is based on the fact that the slope of a line is constant. The slope here is (3+5)/(6-2) = 2.
Now starting from the point (2,-5), pick any other point (x,y) on the line.
The slope between those two points will always be the same: 2. So, for any point (x,y),
(y+5)/(x-2) = 2
(y+5) = 2(x-2)
y+5 = 2x-4
y = 2x-9
You could just as easily use the other point (6,3) as a starting place:
y-3 = 2(x-6)
y-3 = 2x-12
y = 2x-9
To find the equation of a line, you can use the formula for the equation of a line that passes through two points: (x1, y1) and (x2, y2).
The formula for the slope (m) of a line passing through two points is:
m = (y2 - y1) / (x2 - x1)
First, calculate the slope using the given points:
m = (3 - (-5)) / (6 - 2)
m = 8 / 4
m = 2
Now that we have the slope (m), we can use the point-slope form of a linear equation to find the equation of the line:
Y - y1 = m(X - x1)
Using the point (2, -5):
Y - (-5) = 2(X - 2)
Y + 5 = 2X - 4
Simplifying the equation:
Y = 2X - 4 - 5
Y = 2X - 9
Therefore, the equation of the line passing through (2,-5) and (6,3) is Y = 2X - 9. So the correct answer is option D.