Question

A line includes the points (10,1) and (a,-5) has a slope of 1/3. What is the value of a?

Answer 1

For this case we have that by definition, the slope of a line is given by:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

Where:

$(x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})$are two points through which the line passes.

According to the statement we have:

$(x_ {1}, y_ {1}) :( 10,1)\\(x_ {2}, y_ {2}) :( a, -5)\\m = \frac {1} {3}$

Substituting we have:

$\frac {1} {3} = \frac {-5-1} {a-10}\\\frac {1} {3} = \frac {-6} {a-10}\\a-10 = \frac {-6} {\frac {1} {3}}\\a-10 = -18\\a = -18 + 10\\a = -8$

Thus, the value of a is -8.

Answer:

$a = -8$