how do you do this? this is the full question and all info:
"A line with a slope of -3 passes through the point (k,4). Find the y-intercept of the line in terms of k."
I would like to know how to do this along with the answer so i can know im doing it right please!!
Hopefully you know the slope equation: y=mx+b
You know that m=slope, so you can say:
y=-3x+b
next, substitue k for x, 4 for y.
4=-3k+b
b=4+3k
Now, you have an equation.
y=-3x+3k+4
finally, y-intercept is where x=0. So substitue 0 for x.
y=-3(0)+3k+4
y=3k+4
y-intercept is 3k+4
To find the y-intercept of a line in terms of k, we can use the point-slope form of a linear equation: y - y1 = m(x - x1). In this case, the slope is given as -3, and the point is (k, 4).
To find the equation of the line, substitute the values into the point-slope form:
y - 4 = -3(x - k)
Next, simplify the equation by distributing the -3:
y - 4 = -3x + 3k
To find the y-intercept, we need to isolate the y term by rearranging the equation:
y = -3x + 3k + 4
The y-intercept is the value of y when x is equal to 0. So, substitute 0 for x in the equation:
y = -3(0) + 3k + 4
y = 3k + 4
Therefore, the y-intercept of the line, in terms of k, is 3k + 4.