This week in math 10 I learned about point-slope formula. 

So, we already know slope formula which is . So, point-slope form is another way to write this, point-slope form is written as, m(x1-x2) = y2-y1. We can use point-slope formula to achieve slope y-intercept formula, which appears as y=mx+b. 

Example 1: 

So, in this example we start with m=3, “m” is our slope, and because slope is rise over run and 3 is the same thing as 3 over 1 our line will rise by three and run by one. We are also given the coordinates (7,6), we will use these as our coordinates x1 and y1. Because the first number is always the number that will be on the x axis and the second is the number appearing on the y-axis and “m” is 3 we will rewrite our point-slope form equation as, 3(x-7) = y-6. Now we will begin to solve this equation. First, we will distribute the 3 to the x and 7, leaving us with 3x-21=y-6. Now in order to write this equation in slope y-intercept form we need to get “y” alone and to do that we must add 6 to both sides of the equation. We are now left with 3x-15=y, which written the other way, y=3x-15 is the exact formula used for slope y-intercept. 

Example 2: 

So, for this example the slope we are given is m=7, so we rise by 7 and run by 1. Now this time we are given the coordinates (-12,5) now because we are given a negative number it will be a bit more difficult. Now if we remember the formula from above m(x1-x2) = y2-y1. So, we need to remember that when we minus a negative number it becomes an addition question so, 7(x-(-12)) = y-5 is actually 7(x+12) = y-5. So now we will continue the same way we did in the first example by distributing the 7 making our equation, 7x+84=y-5. Now we must add 5 to both sides of the equation to get y all alone. Which will leave us with 7x+79=7, or y+7x+89.