Find a real number, k, such that the line −18x+ky+15=0 has y-intercept −16.
or, stated another way
if x = 0 , y = -16
let's plug it in....
0 + k(-16) + 15 = 0
k = 15/16
To find the value of k, we need to use the given information that the line has a y-intercept of -16.
The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.
Therefore, we substitute x = 0 into the equation -18x + ky + 15 = 0 and solve for k.
-18(0) + k(-16) + 15 = 0
-16k + 15 = 0
Now, solve for k:
-16k = -15
Divide both sides of the equation by -16 to isolate k:
k = -15/-16
k = 15/16
Therefore, the real number k that satisfies the given conditions is k = 15/16.
To find the value of k, we need to use the information given about the line's y-intercept.
The y-intercept is the value of y when x equals 0. In this case, the y-intercept is -16.
Substitute x = 0 and y = -16 into the equation of the line:
-18(0) + k(-16) + 15 = 0
Simplifying the equation:
-16k + 15 = 0
To solve for k, we need to isolate the term with k.
First, subtract 15 from both sides of the equation:
-16k = -15
To isolate k, divide both sides of the equation by -16:
k = -15 / -16
Simplifying the division:
k = 15 / 16
Therefore, the real number k that satisfies the given conditions is k = 15/16.