What is the equation of the line between #(6,5)# and #(2,9)#?

Question

Kennedy Adams · Accepted Answer

#y=-x+11#

The gradient of the line is found using the equation

#m=(y_2-y_1)/(x_2-x_1)#

Substituting #y_1 = 5, y_2 =9 and x_1 = 6, x_2 = 2# we get:

m = #(9-5)/(2-4) = 4/-4 = -1#

Using the formula for a line #y = mx+c# and knowing that # m= -1# and having a point we can work out the equation of the line:

#5 = -1(6)+c# #5 = -6+c# #11=c#

Therefore:

#y = -x+11#

Ethan Adkins · Answer

undefined The equation of the line passing through the points (6,5) and (2,9) can be found using the slope-intercept form equation:

y = mx + b

where m is the slope and b is the y-intercept.

First, calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substitute the coordinates of the points into the formula:

m = (9 - 5) / (2 - 6)
m = 4 / (-4)
m = -1

Now that we have the slope, choose one of the points (let's choose (6,5)) to substitute into the equation along with the slope to find the y-intercept (b):

5 = (-1)(6) + b
5 = -6 + b
b = 5 + 6
b = 11

Now, substitute the slope (m = -1) and y-intercept (b = 11) into the slope-intercept form equation:

y = -x + 11

So, the equation of the line passing through the points (6,5) and (2,9) is y = -x + 11.