How can the line passing through the points (3,5) and (1,4) be written in the slope intercept form?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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