Question

What is the equation of a line, in point- slope form, that passes through (5, −3) and has a slope of 2/3?

I think it's C

Answer 1

You want to find the equation for a line that passes through the point (5,-3) and has a slope of 2/3.

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 2/3. So you can right away fill in the equation for a line somewhat to read:

y=2/3x+b.

Now, what about b, the y-intercept?

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

(5,-3). When x of the line is 5, 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 2/3 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 (5,-3).

So, why not plug in for x the number 5 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!.

(5,-3). y=mx+b or -3=2/3 × 5+b, or solving for b: b=-3-(2/3)(5). b=-19/3.

The equation of the line that passes through the point (5,-3) with a slope of 2/3

is

y=2/3x-19/

Answer 2

Answer:

y+3=2/3(x-5)

Step-by-step explanation: