Question

Determine the equation of a line in standard form that represents alanas training progress. Her progress points corresponds to the points (1,14) and (9,10)

Answer 1

Answer:

The equation of the line passing through the above points is:

$y=-\frac{1}{2}x+\frac{29}{2}$

Step-by-step explanation:

Given:

The two points are: $(x_1,y_1)=(1,14)\textrm{ and }(x_2,y_2)=(9,10)$

The equation of a line when two points are given is:

$y-y_1=\left (\frac{y_2-y_1}{x_2-x_1} \right )(x-x_1)$

Plug in all the values and simplify.

$y-14=\left (\frac{10-14}{9-1} \right )(x-1)\\y-14=\left (\frac{-4}{8} \right )(x-1)\\y-14=-\frac{1}{2}(x-1)\\y-14=-\frac{1}{2}x+\frac{1}{2}\\y=-\frac{1}{2}x+\frac{1}{2}+14\\\\\\y=-\frac{1}{2}x+\frac{29}{2}$

Therefore, the equation of the line passing through the above points is:

$y=-\frac{1}{2}x+\frac{29}{2}$