SOLUTION: What is the equation of the line that passes through the point (3, 2) and has a slope of 4?

Question 465790: What is the equation of the line that passes through the point (3, 2) and has a slope of 4?
Found 3 solutions by kingme18, solver91311, richard1234:
Answer by kingme18(98)   (Show Source): You can put this solution on YOUR website!
I'm going to show you 2 ways to do this.

One is to use slope-intercept form: , where m is the slope and b is the y-intercept. We know the slope for this problem: m = 4. Since every point on the line would work in the equation, we could use your point (3, 2) as (x, y) to solve for b. So, instead of , we can say , and solve for b by multiplying 4*3: , then subtracting 12 on both sides to get b by itself: . Plug that back into . Remember that for the equation, we want the y and the x to still be there--don't use your (3, 2) since that was just one possible point that works. Your final answer is .

Another way to do it is to use point-slope form: . and represent the point you're using; in your case, and . 4 is still m. The nice thing about using this formula is that you don't have to go back and plug in--once you simplify this, you're done! Plug in your numbers: . The first step to simplify is to distribute the 4: . To finish getting y by itself, add 2 to both sides: .

No matter how you do this, your final answer is .
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Use the point-slope form of an equation of a line.

where are the coordinates of the given point and is the given slope.

Note: The result will only be an equation of the desired line. There are many more than one equivalent representations of a given line, hence it is impossible to write the equation of a line.

John

My calculator said it, I believe it, that settles it

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
Use the point-slope form:

This is also equivalent to its slope-intercept form, y = 4x - 10.
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