Answer:
y = -2x + 13
Step-by-step explanation:
Alright we're gonna make this super simple. First, let's assign letters to your coordinates or points given on the line.
Coordinates are represented as (x, y)
(2, 9) --> (x1, y1)
(4, 5) --> (x2, y2)
The slope intercept is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Find Slope
To find the slope (also called m) you will have to do the following: [tex]\frac{y2 - y1}{x2-x1}[/tex]
Super easy, you're just substracting your y values in the numerator and x values in the denominator.
So m = [tex]\frac{5-9}{4-2} =\frac{-4}{2} =-2[/tex]
The slope is, therefore, -2
Our equation is now y = 2x + b. We now have to find b.
Step 2: Find Y-Intercept
To find the y-intercept (also called b) you can plug in any coordinate into the equation found in step 1 and do simple algebra to manipulate the equation and find b.
Let's take coordinate (2, 9). 2 is our x and 9 is our y. Also know that -2 is also our m (or slope). So let's plug all of that information into the slope-intercept formula which is y = mx + b
y = mx + b
9 = -2(2) +b
9 = -4 + b
(add 4 to both sides of the equation to get b)
b = 13
Step 3: Substitute the slope and y-intercept into the slope-intercept formula
y = mx + b
y = -2x + 13
I hope you understood! Good luck :)
