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?

Question

asked Jul 6, 2021 85.3k views

2 Answers

Esteban Brenes · Answer 1 · 2021-07-10T18:41:31+0000

Answer: 5

Explanation:

We can plot given points on graph and join them to make the line make the line.

If the point (a,1) lies on the line, then we can check the point on line corresponding to y=1, and we will get point (5,1). {see attachment}

So, the value of a=5

Alternatively, The equation of the line passing through (a,b) and (c,d) is given by:_

(y-b)=(d-b)/(c-a)(x-a)

So, the equation of the line passing through the points (–4,–2) and (2,0) would be

$(y-0)=(-2-0)/(-4-2)(x-2)\\\\\Rightarrow\ y=(-2)/(-6)(x-2)\\\\\Rightarrow\ y=(1)/(3)(x-2)$

If the point (a,1) lies on the line, then put y=1

$, (1)=(1)/(3)(a-2)\Rightarrow\ 3=a-2\\\\\Rightarrow\ a=3+2=5$

Hence, the required point is (5,1).

Hence, the value of a=5