Question

Which equation is a point slope form equation for line AB ?

Answer 1

Answer:

Answer choice D:

y - 6 = 2(x - 5)

Step-by-step explanation:

This question is basically asking you to find the point-slope form equation for a line going through the points (3, 2) and (5, 6).

As you can tell by the name, point-slope form needs both a point that the line goes through and the slope of the line.

You can find the slope of the line by using the slope formula since you have two points that the line goes through.

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute in the points A and B into the formula.

$m=\frac{6-2}{5-3} \rightarrow\frac{4}{2} \rightarrow 2$

The slope of this line is 2.

Now since we have the slope and a point of the line, we can plug this into the point-slope form equation, which is y - y1 = m(x - x1).

We will be using one of the points (I will be using point A) to substitute the coordinates into y1 and x1, and using the slope to substitute into m.

Substitute point A's coordinates and the slope of the line into the point-slope form equation.

y - (2) = 2(x - (3))

I always put parentheses around the numbers I substitute into an equation to see exactly what is being plugged in, but now you can remove them to find your answer.

y - 2 = 2(x - 3)

Now, since none of the answer choices do not fit with the answer we have found, we can use the other point coordinate-- point B.

Substitute point B and the slope 2 into the equation.

y - (6) = 2(x - (5))

Remove the parentheses.

y - 6 = 2(x - 5)

There is an answer choice for this answer we have found, answer choice D.

By the way, both of the equations we found: y - 2 = 2(x - 3) and y - 6 = 2(x - 5) will yield the same answer in the end so don't worry if one of the points don't work if you have a multiple choice like this question.

Answer 2

Answer: $y-6=2(x-5)$

Step-by-step explanation:

The point-slope form of equation of s line that passes through two points (a,b) and (c,d) is  given by :-

$(y-d)=\dfrac{d-b}{c-a}(x-c)$

Given : A graph with a line running through point A, with coordinates (3, 2), and point B, with coordinates (5, 6).

Then, the a point slope form equation for line AB will be :-

$(y-6)=\dfrac{6-2}{5-3}(x-5)$

$(y-6)=\dfrac{4}{2}(x-5)$

$y-6=2(x-5)$

Hence , equation is a point slope form equation for line AB will be :

$y-6=2(x-5)$