# What is the x and y intercept of the line through (10, 2) and (3, 1)?

electreto05 | College Teacher | (Level 1) Assistant Educator

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First, we find the equation of this line. This can be done by point-slope method in which, we first find the slope and then the intercept of the straight line.

The equation of the line is:

y = m x + b

The slope m  is:

m = (y2 – y1)/(x2 – x1)

For points, P1(10 ; 2) and P2(3 ; 1) the slope is:

m = (1– 2)/(3 – 10) = 1/7

To find the intercept b we substitute the slope in the equation of the line, and substitute x and y, for a given point.

For  P1 (10 ; 2)

2 = 1/7(10) + b   →   b = 4/7

So the equation of the line is:

y = m x + b    →   y = (1/7) x + (4/7)

To find the intercept with y, we substitute x = 0 in the equation:

x = 0   →   y = 4/7

To find the intercept with x, we substitute y = 0 in the equation:

y = 0   →   (1/7) x = -4/7   →   x = -4

justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of a line passing through the 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)` . If the x and y intercepts of a line are a and b, the equation of the line is `x/a+y/b = 1`

Using these formulas, the equation of the line through (10,2) and (3,1) is `(y - 2)/(x-10) = (1-2)/(3-10) = 1/7` .

Rewrite `(y - 2)/(x - 10) = 1/7` in the slope intercept form.

`(y - 2)/(x - 10) = 1/7`

=> 7(y - 2) = x - 10

=> 7y - 14 = x - 10

=> 7y - x = 4

=> `y/(4/7) - x/4 = 1`

The x and y intercept of the line passing through the points (10,2) and (3,1) is -4 and 4/7