Find the equation of the line that passes through (1, 3) and (-1, 4). Find the equation of the line that passes through (1, 3) and (-1, 4).
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We have the points (1,3) and (-1,4) passes through a line.
The equation for the line is:
y-y1 = m (x-x1) where m is the slope.
m= (y2-y1)/(x2-x1)
= (1/-2 = -1/2
y-3= (-1/2)(x-1)
y-3 = (-1/2)x + 1/2
y= (-1/2)x + 1/2 + 3
y= (-1/2)x + 7/2
Multiply by 2:
2y = -x + 7
x + 2y - 7 = 0
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The equation of a line passing through two points `(x_1, y_1)` and `(x_2, y_2) ` is:
`(y - y_1)/(x - x_1) = (y_2 - y_1)/(x _2 - x_1)`
To determine the equation of a line passing through the points (1, 3) and (-1, 4) substitute `x_1 = 1` , `y_1 = 3` , `x_2 = -1` and `y_2 = 4` .
The equation of the line is:
`(y - 3)/(x - 1) = (4 - 3)/(-1 - 1)`
`(y - 3)/(x - 1) = -1/2`
2*(y - 3) = -1(x - 1)
2y - 6 = -x + 1
x + 2y - 7 = 0
The required equation of the line is x + 2y - 7 = 0
We'll find the equation of the line that passes through the given points, using the formula:
(x2-x1)/(x-x1) = (y2-y1)/(y-y1)
Now, we'll substitute the coordinates of the given points, into the formula above:
(-1-1)/(x-1) = (4-3)/(y-3)
-2/(x-1) = 1/(y-3)
We'll cross multiply:
-2(y-3) = x-1
-2y + 6 = x-1
-2y = x-1-6
-2y = x-7
We'll divide by -2:
y = -x/2 + 7/2
So, the equation of the line is: y = -x/2 + 7/2
The line passing through the points (x1, y1) and (x2 y2) is given by:
(y-y1)/(y2-y1) = (x-x1)/(x2-x1).............(1)
(x1,y1) = (1,3) and (x2,y2) = (-1 , 4). Substituting these given coordinates in (1) we get:
(y-3)/(4-3) = (x-1)/(-1-1)
(y-3)/-1 = (x-1)/-2
2(y-3) = (x-1)
2y-6 = x-1.
x-1-2y+6 = 0
x-2y -5 = 0 is the line that passes through (1,3) and (-1,4).
A general equation of a line is:
y = mx + c
Where:
y = slope of the line
And c is a constant.
The slope of a line joining two points (x1, y1) and (x2, y2) is given by:
slope = m = (y2 - y1)/(x2 - x1)
Substituting given values of x1, y1, x2, and y2 in the above equation of slope:
m = (4 - 3)/( -1 - 1) = -1/2
Substituting this value of m in the general equation of line:
y = -x/2 + c ... (1)
To find the value of c we substitute values of x1 and y1 in the above equation (1):
3 = -1/2 + c
==> c = 3 + 1/2 = 7/2
Substituting this value of c in equation (1):
y = -x/2 + 7/2
This equation can be simplified as:
x + 2y = 7
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