Answer:
Step-by-step explanation:
The slope-intercept from of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁, y₁), (x₂, y₂) - ponts on a line
We have two points (7, 9) and (2, -3).
Substitute:
[tex]m=\dfrac{-3-9}{2-7}=\dfrac{-12}{-5}=2.4[/tex]
Put the value of the slope and the coordinates of the point (7, 9) to the equation of a line:
[tex]9=2.4(7)+b[/tex]
[tex]9=16.8+b[/tex] subtract 16.8 from both sides
[tex]-7.8=b\to b=-7.8[/tex]
Finally we have:
[tex]y=2.4x-7.8[/tex]
Answer:
y= 12/5x-7.8
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. What do we need such as information? And do we have any information to help us out? Yes to both questions! Well what is it? Well we are given two points or coordinate points.
(2,-3) and (7,9)
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.
(2,-3) and (7,9)
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!
2= x₁ -3=y₁ 7= x₂ 9= y₂ we have them labeled now
next let put them in the equation correctly
(9-(-3) divided by (7-2) (REMEMBER THIS!! => (a negative number subtracted by a negative number makes it a positive so... -(-3)= +3) So...
(9+3) divided by 5 subtract 2 from 7 and you get 5
12 divided by 5 <= this is your slope!! But as a fraction it would be positive 12 over a positive 5!!
So we now now what the slope is, check :D
y= outcome
m= slope => 12/5
b= y-intercept
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 (7,9) coordinate point.
How do we do this well 7 is "x" and 9 is "y". Let substitute the letters with the coordinate points. So...
At first with the slope...
y=12/5x+b
With coordinate points and slope
9=12/5(7)+b
Now it's time for some algebra!!! Yeah!!!
9=12/5(7)+b 1. multiple if there is anything to multiple
9=16.8+b 2. we need to get b alone! So we need to subtract 35 from both sides
9 =16.8+b
-16.8 -16.8
-7.8= b yes! We have b alone!
In this case we take in all the information we got!
y= outcome
m= slope => 12/5
b= y-intercept => -7.8
So the equation or line is...
y=12/5x-7.8
I really do hope this helps you! And I'm deeply sorry that it took me a very long time! I do have a photo attached that helped me check if I was correct or not! I will have it attached promise! Also I used the Desmos graphing calculator! Which is the best thing! (No joke) If you ever need to ask anything don't be afraid to comment or message me! I hope you have a great day!!
Oh and I also have a link that will include the points and will take you exactly to the Desmos website!
