Final answer:
To find the missing value (y) in the linear equation (10, y) and (3, 4) with a slope of -2/7, we can use the formula y = mx + b. By solving for the y-intercept (b) using the coordinates (3, 4), we can then determine the equation of the line. Substituting x = 10 into this equation will give us the missing value, y.
Step-by-step explanation:
To find the missing value in the given linear equation, (10, y) and (3, 4), we need to determine the equation of the line represented by these two points. From the information provided, we know that the slope of the line, m, is -2/7. Using the formula y = mx + b, where m is the slope and b is the y-intercept, we can solve for b using the coordinates (3, 4). Plugging in the values of x = 3, y = 4, and m = -2/7, we get 4 = (-2/7)(3) + b. Solving for b, we find b = 4 + 6/7 = 34/7. Therefore, the equation of the line is y = (-2/7)x + 34/7.
To find the missing value, we substitute x = 10 into the equation y = (-2/7)x + 34/7. Evaluating this expression, we find y = (-2/7)(10) + 34/7 = -20/7 + 34/7 = 14/7 = 2. Therefore, the missing value is y = 2.