Final answer:
To find the value of x that would result in line a being parallel to line b, we need to compare their slopes. Line a has a slope of 3, while line b has a slope of 10x + 8. We can equate the two slopes and solve for x.
Step-by-step explanation:
To find the value of x that would result in line a being parallel to line b, we need to compare their slopes. Line a has a slope of 3, which means its equation is y = 3x + b. Line b has a slope of 10x + 8, which means its equation is y = (10x + 8)x + b. In order for the two lines to be parallel, their slopes must be equal. Therefore, we can equate the two slopes:
3 = (10x + 8)x
Now solve for x:
3 = 10x^2 + 8x
0 = 10x^2 + 8x - 3
Using the quadratic formula, the solutions are x = -1 and x = 0.3. Since we are dealing with a line, we can disregard the negative solution. Therefore, the value of x that would result in line a being parallel to line b is x = 0.3.