Question

Use the interactive to graph the line that goes through the points (–4,–2) and (2,0). The point (a,1) lies on the line you graphed. What is the value of a?

Answer 1

The equation of the line passing through points $A(x_1,y_1), B(x_2,y_2)$ is:
$y= \dfrac{y_2-y_1}{x_2-x_1}(x-x_1) +y_1$.

If A(-4,-2) and B(2,0), then 
$y= \dfrac{0-(-2)}{2-(-4)}(x-(-4))+(-2) \\ y= \dfrac{2}{6} (x+4)-2 \\ y= \dfrac{1}{3} x- \dfrac{2}{3}$.

If point (a,1) lies on the line

$y= \frac{1}{3} x- \frac{2}{3}$,

then

$1=\dfrac{1}{3} a- \dfrac{2}{3} \\ \dfrac{5}{3} =\dfrac{1}{3} a \\ a=5$.

Answer: $y= \frac{1}{3} x- \frac{2}{3}$, a=5.

Answer 2

Answer:

the answer is 5!

Step-by-step explanation:

just did it and it was rightt