amount borrowed\tamount repaid\n$100\t$135\n$200\t$260\n$500\t$635\n$800\t$1,010\nwhich equation represents…

amount borrowed\tamount repaid\n$100\t$135\n$200\t$260\n$500\t$635\n$800\t$1,010\nwhich equation represents the relationship?\n$y = \\frac{5}{4}x$\n$y = \\frac{4}{5}x$\n$y = \\frac{5}{4}x + 10$\n$y = \\frac{4}{5}x+55$
Answer
Answer:
y = \frac{5}{4}x + 10
Explanation:
Step1: Let amount borrowed be (x) and amount repaid be (y).
Let (x) be the independent - variable and (y) be the dependent - variable.
Step2: Assume the linear equation (y=mx + b).
The general form of a linear equation is (y = mx + b), where (m) is the slope and (b) is the y - intercept.
Step3: Calculate the slope (m) using two points ((x_1,y_1)) and ((x_2,y_2)).
Take ((x_1 = 100,y_1 = 135)) and ((x_2 = 200,y_2 = 260)). The slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{260 - 135}{200 - 100}=\frac{125}{100}=\frac{5}{4}).
Step4: Substitute (m), (x), and (y) into (y=mx + b) to find (b).
Using the point ((x = 100,y = 135)) and (m=\frac{5}{4}), we have (135=\frac{5}{4}\times100 + b). Then (135 = 125 + b), so (b=135 - 125=10).
Step5: Write the equation.
The equation is (y=\frac{5}{4}x + 10).