What is the equation of the line that passes through (6,11) ,( - 1,2)?

Question

3936 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-12T05:28:01

$color(blue)(y=9/7x+23/7)$

We are given two points : -

$color(red)((6, 11), (-1, 2)$ .... Points

Let, $color(green)(x_1 = 6 and y_1 = 11)$

Let, $color(green)(x_2 = -1 and y_2 = 2)$

Hence, the two points given to us can be written as

$color(red)((x_1, y_1), (x_2, y_2)$ .... Points

We will next find the Slope using the formula:

$color(green)(Slope(m) = (y_2 - y_1)/(x_2-x_1))$

$rArr Slope(m) = ( 2- 11)/(-1--6)$

$rArr (-9)/(-7) = 9/7$

Therefore,

$Slope(m) = 9/7$

The Point-Slope Equation of a Straight Line is given by:-

$color(green)((y - y_1) = m(x-x_1))$ Formula.1

We can substitute the value of $Slope(m) = 9/7$ in the equation above.

We also need a Point.

We will choose one the points given to us: $(6, 11)$

This point $(6, 11)$ is our $(x_1, y_1)$ .

We are ready to use the Point-Slope Equation of a Straight Line using Formula.1

Substitute the values of $m$ and $(x_1, y_1)$ .

$y-11 = 9/7(x-6)$

$rArr y - 11 = 9/7x-54/7$

$rArr y = 9/7x + 23/7$

Hence, the Equation of a Straight Line passing through the points $color(red)((6, 11), (-1, 2)$ is given by:-

$color(blue)(y = 9/7x + 23/7)$

Graph below has the equation of the straight line we found:

enter image source here