How do you find the value of r such the points (6,-2), (r,-6) has slope m=4?

1 Answer
Geoff K.
Feb 15, 2017

By starting with the slope formula #m=(y_2-y_1)/(x_2-x_1)#, plugging in the known values, and solving for the one remaining.

#r=5#.

Explanation:

The slope #m# of a line that connects point #(x_1, y_1)# and point #(x_2, y_2)# is "how fast #y# changes relative to how fast #x# changes". As a formula, this is

#m=(Delta y)/(Delta x)=(y_2-y_1)/(x_2-x_1)#

We are given

#(x_1,y_1) = (6, "–"2)#,
#(x_2,y_2) = (r, "–"6)#, and
#m=4#.

All we need to do is plug these into our slope formula and solve for #r#:

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

#=>4=("–"6-("–"2))/(r-6)#

#=>4(r-6)="–"6+2#

#=>r-6=("–"4)/4#

#=>r="–"1+6#

#=>r=5#

So in order for the line connecting #(6,"–2")# and #(r,"–6")# to have a slope of #4#, we need #r=5#.

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