A line has a slope of m = -1/3
and passes through the points (-4,k) and (2,3). Fine the value of k
y=-1/3 + b
3=-1/3(2)+b
3=-2/3+b
11/3 = b
y=-1/3X +11/3
y=-1/3(4)+11/3
y=15/3 or 5
y is the same as k so k=5
Thank you so much! What I did wrong was pluck in the wrong equation
To find the value of k, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m represents the slope of the line, and b represents the y-intercept.
Given that the slope of the line is m = -1/3, and the line passes through the points (-4, k) and (2, 3), we can use either of these points to find the value of k.
Let's use the point (-4, k) in the equation:
y = mx + b
Substituting the x and y values from the point (-4, k):
k = (-1/3)(-4) + b
k = 4/3 + b
To find the value of b, we need another point on the line. Let's use the point (2, 3):
3 = (-1/3)(2) + b
3 = -2/3 + b
Adding 2/3 to both sides:
3 + 2/3 = b
Simplifying:
9/3 + 2/3 = b
11/3 = b
Now that we have the value of b, we can substitute it back into the equation to find the value of k:
k = 4/3 + (11/3)
k = (4 + 11)/3
k = 15/3
k = 5
Therefore, when the slope of the line is m = -1/3 and the line passes through the points (-4, k) and (2, 3), the value of k is 5.