Question

Which is an equation of the line that passes through the point (2, 3) and has a slope of 1/3

Answer 1

Answer:

You want to find the equation for a line that passes through the point (2,3) and has a slope of 1/3.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 1/3. So you can right away fill in the equation for a line somewhat to read:

y=1/3x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(2,3). When x of the line is 2, y of the line must be 3.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 1/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (2,3).

So, why not plug in for x the number 2 and for y the number 3? This will allow us to solve for b for the particular line that passes through the point you gave!.

(2,3). y=mx+b or 3=1/3 × 2+b, or solving for b: b=3-(1/3)(2). b=7/3.

The equation of the line that passes through the point (2,3) with a slope of 1/3

is

y=1/3x+7/3

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