What is the slope between #(-3 , 3)# and #(5, 11)#?

2 Answers
Jim G.
Jun 5, 2018

#"slope "=1#

Explanation:

#"calculate the slope using the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(-3,3)" and "(x_2,y_2)=(5,11)#

#m=(11-3)/(5-(-3))=8/8=1#

Mark S.
Jun 5, 2018

The slope of the line between #(-3,3)# and #(5,11)# is #1#.

Explanation:

To calculate the slope/gradient of a linear function when we are given two coordinate points on the line, we can use the formula for linear gradient:

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

Essentially, this formula gives us the ratio between the change in #y# and the change in #x# between the two coordinates.

mathisfun.com

So, this formula accounts for two sets of coordinates, #(x_1, y_1)# and #(x_2, y_2)#. We simply need to substitute your points into these:

#(-3, 3) -> (x_1, y_1)#
#(5, 11) -> (x_2, y_2)#

Hence:

#x_1 = -3#
#x_2 = 5#
#y_1 = 3#
#y_2 = 11#

Now, we substitute these into the formula and simplify:

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

#=(11-3)/(5-(-3))#

#=(11-3)/(5+3)#

#=(8)/(8)#

#=1#

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