What is the value of k if the point (5,k) is on the line 2y+3x = 7?

Answer 1

2y+3x = 7 (5,k) is on the line, plug it into the equation

2k+3(5) = 7

2k = 7-15 = -8

k = -8/2 = -4

(5,-4) is a point on the line

or 2y+3x = 7

2y =-3x + 7

y = (-3/2)x +7/2 is a downward sloping line with slope =-3/x and y intercept = 7/2 = the point (0, 7/2)

the x intercept = 7/3, the point (7/3, 0). Plot the two intercepts and connect them with a straight line. when x=5, the line is going below the x axis into quadrant IV, where y<0, where <k

for every 1 unit increase in x, y decreases by 3/2. x increases from 7/3 to 5, from 2 1/3 to 5, a 2 2/3 increase or 8/3. 8/3 times -3/2 = (8/3)(-3/2) = -4 = k

Answer 2

Hey Michael!

If you recognize (5, k) as the X and Y coordinates in the problem, you can substitute these values for "X" and "Y" in the equation:

Original Equation: 2y + 3x = 7

Substitute Values: 2(k) + 3 (5) = 7

Multiplication: 2k + 15 = 7

Subtract 15 from both sides: 2k = -8

Dive both sides of the equation by 2: k = -4

Hope this helps!