Write an equation of given line through the two points (4,1) (3,-1)

Question

asked Jun 21, 2022 184k views

1 Answer

Maxm · Answer 1 · 2022-06-27T06:54:47+0000

Answer:

y=2x-7

Explanation:

The equation for a straight line is

y=mx+c

where m is the gradient and c is the y-intercept.

To have the full equation, we need to find m and c values.

To find m, the formula is

(y_(2)-y_(1) )/(x_(2)-x_(1) )

By substituting the two points (4,1) and (3,-1) into the formula, we get:

$m =(-1-1)/(3-4) \\m=(-2)/(-1) \\m=2$

Now we have
y=2x+c

To solve for c, substitute any of the two points in to the equation. Let's say we insert (4,1) into the equation:

$y=2x+c\\1=2(4)+c\\c=1-8\\c=-7$

Therefore, the full equation is

y=2x-7

Pro tip:

You can always substitute (4,1) or (3,-1) to check if the equation is correct.