Question

Write an equation of the line that passes through a pair of points:
(-3,-1), (2, 2)

Answer 1

The equation of the line that passes through the points (-3,-1) and (2, 2) is calculated by first finding the slope, which is 3/5, and then using the point-slope form to write the equation as y = (3/5)x + 4/5.

Step-by-step explanation:

To write the equation of a line that passes through the points (-3,-1) and (2, 2), the first step is to calculate the slope (m) of the line. This can be done using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the given points. In this case, the slope is m = (2 - (-1)) / (2 - (-3)) = 3 / 5.

Next, you can use the point-slope form of the equation: y - y1 = m(x - x1). Plugging in one of the points (-3, -1) and the calculated slope 3/5, the equation becomes y - (-1) = (3/5)(x - (-3)), which simplifies to y + 1 = (3/5)x + 9/5. Finally, to put it in the slope-intercept form (y = mx + b), we solve for y to get y = (3/5)x + 9/5 - 1, which simplifies to y = (3/5)x + 4/5.

Thus, the equation of the line that passes through the points (-3,-1) and (2, 2) is y = (3/5)x + 4/5.

Answer 2

Step-by-step explanation:

First off, what do we know about a equation that involves the slope and y-intercept form? Well is there a formula? Yes, there is! So what is it? The formula is called a linear equation. It is y=mx+b . What do these symbols or variables represent? Well they represent the things that makes a line.

y= outcome

m= slope

b= y-intercept

So we know that now right? Hopefully so. Let's go to the next step. We are given two points or coordinate points.

(-3, -1) and (2, 2)

Now you may be think, "Okay yippie how do we still find the slope!?" Well here's the thing, there's another equation involved (gasp). This equation actually helps us to find "m" or the slope of the equation. The formula is y₂₋y₁ divided by x₂-x₁. So now look at the two coordinates or points we are given.

They both have an x and y, correct? Correct! But here's the thing. The first coordinate points will be 1 and the second one will be 2. So let us label these points!

-3= x₁ -1=y₁ 2= x₂ 2= y₂ we have them labeled now.

Next let put them in the equation correctly

(2-(-1) divided by (2-(-3)

(REMEMBER THIS!! => a negative sign in front of a negative sign during multiplication would result the number becoming positive!!!)

=> -(-1) = + 1 and -(-3) = +3

(2+1) divided by (2+3)

3 divided by 5

Can you make this even smaller? No you can. So this is the final answer! This is your slope of the equation!! Aka "m"

But what about the "b" or the y-intercept? How do we find that? What is the y-intercept anyways? Well the y-intercept is where the line on a graph crosses the y axis. In which case what is "x" when "y" is zero. => (x, 0)

In this case we can actually use one of the coordinate points we are already given. Let us use the (2, 2) coordinate point.

How do we do this? well 2 is "x" and 2 is "y". Let substitute the letters with the coordinate points. So...

At first what is the equation with the slope we found? It is y= 3/5x+b...

Now we need to input the "x" and "y" of the coordinate points into the equation.

2 = 3/5 (2) +b

The main goal is to get "b" all alone on one side of the equation to get the final equation!

1. We need to multiple the slope with the x value

2 = 3/5 (2) +b

2 = 1.2 +b (Side note! 1.2 can also equal to 6/5!!)

2. Next we need to get b alone! We have to get 1.2 on the other side. How? Well let's do the opposite of adding!! We subtract!

2 = 1.2 +b

-1.2 -1.2

0.8 = b

And there we go we have our "y-intercept"!!

Now final we can form the equation we been waiting for!!

y= 3/5x+0.8

I really do hope this helps you! And I'm deeply sorry that it took me a very long time! And if you even need to make sure something looks right as in on a graph? Try to use Desmos! I love that website and I still use it til this day! I hope you have a great day!!