What is the slope- intercept form of the line that passes through (9,20) ans (7,18)?

Answer 1

Hi Funky C. !

So to start out solving this we will need a few equations to work off of.

1) y=mx + b where m = slope and b = the y-intercept

2) m = (y₂-y₁)/(x₂-x₁) is the slope equation where (7,18) = (x₂,y₂) and (9,20) = (x₁,y₁) respectively.

3) y-y₁=m(x-x₁) is called point slope form which will help us put all this into the form y = mx +b

Basically, from here it's just plugging in numbers and solving each equation until it's in slope-intercept form.

The easiest way to do it is to start with your slope equation first and then go to point slope form.

Slope equation:

m = (y₂-y₁)/(x₂-x₁)

y₂ = 18, y₁ = 20, x₂ = 7 and x₁ = 9

We will go ahead and plug in all the coordinates in their right places and simplify until we get a fraction.

m = (18-20)/(7-9) = (-2/-2) = +1

We now have a slope of positive one, m=1, so we will use this in our point slope form equation.

Point Slope Form:

y-y₁=m(x-x₁)

Let's go ahead and replace y₁ , x₁ and m with the numbers we are given. The y and the x can stay alone. Note that the x and y are different from y₁ and x₁.

y-20=1(x-9)

Now that we've replaced these variables with numbers, we will use the distributive property and combining like terms to solve for y. Remember that our goal is to solve for y so we can have the equation in slope intercept form.

1) distributive property:

we will just distribute the 1 (the slope) to the x and the -9.

y-20 = 1*x + 1*(-9)

y-20 = x - 9

2) we will combine like terms by adding 20 to both sides. This in turn will isolate y by itself and nicely situate itself into the form of y=mx +b

y-20 +20 = x - 9 +20

y = x + 11

So finally after all these equations we have arrived at y = x + 11 where we have a slope of 1 (the 1 in front of the x is invisible because mathematicians think it's redundant to put it there. It's kind of like saying "I'm going to eat ONE apple" instead of saying "I'm going to eat an apple". They mean the same thing it's just one sounds less weird. In math saying "x" by itself is equivalent to "one x" but "x" rolls off the tongue better) and a y-intercept of 11.

I hope this was helpful, let me know if you have any other questions. Good luck and have fun!

Answer 2

(9,20) (7,18)

line through those 2 points has slope (20-18)/(9-7) = 2/2 = 1

y=mx + b where m=1 and b is calculated by plugging in either point

18=(1)(7) + b

b = 18-7 = 11

y=x+11 is the equation of the line through the given two points