Answer:
The equation of the line that passes through the point (9,51) with a slope of 5
is
y=5x+6
Explanation:
You want to find the equation for a line that passes through the point (9,51) and has a slope of 5.
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 5. So you can right away fill in the equation for a line somewhat to read:
y=5x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(9,51). When x of the line is 9, y of the line must be 51.
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 5 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 (9,51).
So, why not plug in for x the number 9 and for y the number 51? This will allow us to solve for b for the particular line that passes through the point you gave!.
(9,51). y=mx+b or 51=5 × 9+b, or solving for b: b=51-(5)(9). b=6.