Question

Write the equation of a line that passes through the point (1,4) and has a slope of 9.

Answer 1

Answer:

y=9x-5

Step-by-step explanation:

You want to find the equation for a line that passes through the point (1,4) and has a slope of 9.

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

y=9x+b.

Now, what about b, the y-intercept?

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

(1,4). When x of the line is 1, y of the line must be 4.

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 9 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 specifically passes through the point (1,4).

So, why not plug in for x the number 1 and y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.

(1,4). y=mx+b or 4=9 × 1+b, or solving for b: b=4-(9)(1). b=-5.The equation of the line that passes through the point (1,4) with a slope of 9

is

y=9x-5