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

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: