Question

Write an equation in standard form of the line that passes through the point (9, 2) with a slope of 1/3

Answer 1

Answer:

y=1/3x-1

Step-by-step explanation:

You want to find the equation for a line that passes through the point (9,2) 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:

(9,2). When x of the line is 9, y of the line must be 2.

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 (9,2).

So, why not plug in for x the number 9 and for y the number 2? This will allow us to solve for b for the particular line that passes through the point you gave!.

(9,2). y=mx+b or 2=1/3 × 9+b, or solving for b: b=2-(1/3)(9). b=-1.

The equation of the line that passes through the point (9,2) with a slope of 1/3

is

y=1/3x-1