Find the equation for the line that passes through the points (-1,-3) and (3,3)

Answer 1

Hello Sandra,

The minimum number of points needed to determine the equation of a line is two and that is exactly what you have been given!

To find the equation you need two components:

1) The slope

2) The y-intercept.

Assuming you need the answer in slope-intercept form which is y = mx + b, where m represents the slope and b is the y-intercept.

The slope is: the difference of the y-values divided by the difference in the x-values. So using (3,3) as the "first" point and (-1, -3) as the "second" point.

m = 3 -(-3) = 3 + 3 = 6 = 3 So the slope is 3/2!

3 - (-1) 3 + 1 4 2

So we can replace the m in the equation - y = 3/2 x + b. So now we just need to find the "b" or the y-intercept.

To do this we can choose either point and substitute the x and y values into the equation. I will choose (3,3).

3 = (3/2) (3) + b

3 = 9/2 + b

6/2 = 9/2 + b

6/2 - 9/2 = b

b = -3/2

Now we can substitute the value we found for b into the equation! y = 3/2 x - 3/2

I hope this helps!!

Caroline

Answer 2

The equation of a line is given by:

y = ax + b

Our goal here is to determine those parameters a and b such that the line y = ax + b passes through the two given points.

In other words, the line equations needs to be satisfied for the points (-1,-3) and (3,3).

Let us start with the first point. Plugging the x, y values into the line equation gives us:

-3 = -1*a + b ⇔ - a + b = -3

In addition, the second point will give us:

3 = 3*a + b

Using these two new equations we can solve for a and b. Indeed, the first equation gives us b = a - 3, so if we plug this into the second equation, we get

3 = 3*a + a - 3 ⇔ 4*a = 6 ⇔ a= 1.5

and then b = -1.5.

As a result, the line equation we are looking for is

y = 1.5*x - 1.5

To verify your answer, you can plug in the two points to make sure that the equation still holds:

1. For (-1,-3), we get -3 = 1.5*(-1) - 1.5 = -3 (true)
2. For (3,3), we get 3 = 1.5*3 - 1.5 = 3 (true)

I hope this was helpful. If you have any more questions, please feel free to reach out to me!

Answer 3

Remember the equation of a line in slope y-intercept form is

y = mx + b

you need to find the value of m (the slope or gradient) and the value of b (the y intercept, the value of y when x=0)

m=. (y2 - y1)/(x2 - x1) = (-3 - 3)/(-1 - 3) = -6/-4 = 3/2

Now, substitute that into the equation for m, and you can choose either given point and use it to sub into x and y. Then you solve to find b.

In this case, it’s easier to use (3, 3)

so now…

y = mx + b

3 = (3/2)3 + b

3 = (9/2) + b

3 - (9/2) = b

-1.5 = b

y= mx + b

y= (9/2)x + -1.5