What is the equation of the line between the points (4,3 ) and ( 7, 9)?

hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the points ( 4,3) and ( 7,9). We need to find the equation of the line that passes through the points.

We will write the equation into the standard form.

==> y-y1 = m (x-x1) where (x1,y1) is any point passes through the line and m is the slope.

We will calculate the slope.

==>m = ( y2-y1) / (x2-x1) = ( 9-3)/(7-4) = 6/3 = 2

==> m = 2

Now we will substitute with the slope m =2 and the point ( 4,3).

==> y-3 = 2 (x-4)

==> y-3 = 2x -8

==> y= 2x -8 + 2

==> y= 2x -5

==> y-2x + 5 = 0

justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation between the two points (x1, y1) and (x2, y2) is given by (y – y1) = [(y2-y1) / (x2 – x1)]*(x – x1).

Here we have the two points (4, 3) and (7, 9). This gives x1 = 4, x2 =7, y1 = 3 and y2 = 9.

Substituting the values in (y – y1) = [(y2-y1) / (x2 – x1)]*(x – x1)

=> (y – 3) = [(9 – 3) / (7 – 4)]*(x – 4)

=> y – 3 = (6/3)*(x – 4)

=> y – 3 = 2x – 8

The required line is y – 2x + 5 = 0.