Question

what is the value of a if the line passes through (a,7) and (1,a) has a slope of -5/9

Answer 1

y=-5/9x + b
Substitute the points in the equation to give you two equations.
1. 7=-5a/9 + b
2. a= -5/9(1) + b
Then solve using either substitution or elimination.

Answer 2

Value of $\boldsymbol{a}$ is $\boldsymbol{\frac{29}{2}}$

Slope of a line defined its steepness.

Slope of a line passing through points $\boldsymbol{(x_1,y_1),(x_2,y_2)}$ is given by $\boldsymbol{\frac{y_2-y_1}{x_2-x_1}}$

Take $\boldsymbol{(x_1,y_1)=(a,7)}$

Take $\boldsymbol{(x_2,y_2)=(1,a)}$

Also,

Slope $(m)=\frac{-5}{9}$

          $\boldsymbol{m=\frac{y_2-y_1}{x_2-x_1}}$

          $\frac{-5}{9} =\frac{a-7}{1-a}$

$-5(1-a)=9(a-7)$

  $-5+5a=9a-63$

          $4a=58$

            $a=\frac{58}{4}$

           $\boldsymbol{a=\frac{29}{2}}$

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