Answer:
To find the value of k and the equation of the line, we can use the slope-intercept form of a line: y = mx + b, where m is the slope of the line, and b is the y-intercept.
The slope of the line (m) is given as -⅔. To find the y-intercept (b), we can substitute one of the given points and the value of m into the equation.
Let's use the point (3,k) :
y = mx + b
k = -⅔ * 3 + b
k = -2 + b
b = k + 2
Now we have the equation of the line in the slope-intercept form: y = -⅔x + (k + 2)
To find the value of k we can use the other point (-3, 2k) and substitute into the equation:
2k = -⅔(-3) + (k + 2)
2k = 2 + k + 2
k = -2
So the value of k is -2 and the equation of the line is y = -⅔x + (k + 2) = -⅔x - 2
This line is a straight line with the slope of -⅔ which passes through the points (3, k) and (-3, 2k) and its equation is y = -⅔x - 2