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# Find \$a\$ if the point \$(3,a)\$ is on the line that passes through \$(-2,7)\$ and \$(5,-3)\$.

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Find \$a\$ if the point \$(3,a)\$ is on the line that passes through \$(-2,7)\$ and \$(5,-3)\$.

Nov 19, 2017

#1
+7348
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the slope between  (-2, 7)  and  (5, -3)   =   [ -3 - 7 ] / [ 5 - -2 ]   =   -10/7

And since  (3, a)  lies on the same line as those two points, then we know.....

the slope between  (3, a)  and  (-2, 7)   =   -10/7

[ 7 - a ] / [ -2 - 3 ]   =   -10/7

[ 7 - a ] / [ -5 ]   =   -10/7            Multiply both sides by  -5 .

7 - a   =   50/7                           Subtract  7  from both sides.

-a   =   50/7 - 7

-a   =   50/7 - 49/7

-a   =   1/7

a   =   -1/7                    And here's a graph:  https://www.desmos.com/calculator/prq2oggmcv

Nov 20, 2017

#1
+7348
+1

the slope between  (-2, 7)  and  (5, -3)   =   [ -3 - 7 ] / [ 5 - -2 ]   =   -10/7

And since  (3, a)  lies on the same line as those two points, then we know.....

the slope between  (3, a)  and  (-2, 7)   =   -10/7

[ 7 - a ] / [ -2 - 3 ]   =   -10/7

[ 7 - a ] / [ -5 ]   =   -10/7            Multiply both sides by  -5 .

7 - a   =   50/7                           Subtract  7  from both sides.

-a   =   50/7 - 7

-a   =   50/7 - 49/7

-a   =   1/7

a   =   -1/7                    And here's a graph:  https://www.desmos.com/calculator/prq2oggmcv

hectictar Nov 20, 2017