Final answer:
Five solutions for the linear equation -x + 3/4y = -6 include (0,-8), (4,-2.75), (8,1.5), (12,4.5), and (16,7.5), which were found by substituting different values of x and solving for y.
Step-by-step explanation:
A student asked for five solutions for a linear equation -x + ¾ y = -6. Linear equations are represented in the form y = mx + b, where m is the slope and b is the y-intercept. Here are five solutions for the equation provided:
- When x = 0, ¾ y = -6, so y = -8.
- When x = 4, -4 + ¾ y = -6, so y = ¾(-6 + 4) = -2 ¾ or -2.5.
- When x = 8, -8 + ¾ y = -6, so y = ¾(2) = 1.5.
- When x = 12, -12 + ¾ y = -6, so y = ¾(6) = 4.5.
- When x = 16, -16 + ¾ y = -6, so y = ¾(10) = 7.5.
Each pair of numbers (x,y) represents a solution to the equation, where x is the independent variable and y is the dependent variable. We can generate solutions by choosing values for x and then solving for y.