Item 4 Write in slope-intercept form an equation of the line that passes through the given points. (2, 4), (3, 6)

Answer 1

Hello Madison,

The first thing that I like to do is to understand what I am needing to get to, so for this question, the goal is to get to the slope intercept form.

1. y = mx + b

So now that we know that m is for slope, and b is for the y intercept, lets get started on the question.

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Let's figure out the slope, to determine the slope we look for rise (y coordinates) over run (x coordinates)

y₂ - y₁

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x₂ - x₁

We have 2 points on this line (2,4) and (3,6) lets give them identifiers so we can put them into our slope formula.

1. 2 = x₁
2. 4 = y₁
3. 3 = x₂
4. 6 = y₂

From here we just simplify

6-4 = 2 (this is y₂ - y₁)

3-2 = 1(this is x₂ - x₁)

So for our slope we have 2/1 which simplifies just to 2.

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I have great news Madison, we're almost done!

We started with the base Slope Intercept form, but now we can insert our slope.

y=2x+b

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Now we need to determine if there is a y intercept (which is equal to b).

The issue we have at hand is that we have 3 variables, y, x, and b... but if we read the question, the problem provides us with two sets of x and y coordinates, so we can easily plug these in.

I am going to choose the first coordinates to find the y intercept, then use the second coordinates to verify my answer

4=2(2)+b // our first coordinates are (2,4) we substitute y for 4, and substitute x for 2

4 = 4 + b // simplify, and move b by itself

0 = b // our y intercept should be equal to 0

Lets verify

6 = 2(3) + b // second coordinates are (3,6) so substitute y for 6, and x for 3

6 = 6 + b // simplify

0 = b // great news, we were right!

Ok great, my y intercept(which is defined as b) should be equal to 0

So lets wrap this problem up!

Initially we were asked to an equation in slope intercept form with the two points we were given

y = mx + b

we found the slope (m) was 2

y = 2x + b

and we found that the y intercept (b) was 0

y = 2x + 0

So finally, we just simplify this to:

y = 2x

I hope this explanation helps, if you have any questions please feel free to reply!