How can the line passing through the points (3,5) and (1,4) be written in the slope intercept form?
The equation of a line passing through the points (x1, y1) and (x2 , y2) is given by
(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)
Here we have x1 = 3, x2 = 1 , y1 = 5 and y2 = 4.
Substituting the values:
y - 5 = [-1 / -2]( x - 3)
=> y - 5 = (1/2)(x - 3)
=> 2y - 10 = x - 3
=> 2y = x + 7
Now this is the equation in the slope intercept form. The slope is (1/2) and the y intercept is (7/2).
=> y = x / 2 + 7/2
I suppose that you want to write the slope intercept form of the equation of the line that passes through the given points.
The slope intercept form is:
y = mx + n, where m represents the slope and n is the y intercept.
Now, we know that the equation is determined if we know the coefficients m and n.
We also know that a point is on the line, if and only if the coordinates of the point are verifying the equation of the line.
5 = 3m + n (1)
4 = m + n (2)
We'll subtract (2) from (1) to elimiante n:
3m + n - m - n = 5 - 4
2m = 1
We'll divide by 2:
m = 1/2
Now, we'll substitute m in (2):
1/2 + n = 4
We'll subtract 1/2:
n = 4 - 1/2
n = 7/2
Now, we can write the slope intercept form of the line that is passing through the given points:
y = x/2 + 7/2