Question

complete the equation of the line through (3, -1) and (4, 7). use exact numbers. y =

Explanation:

Step1: Find the slope (m)

The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1,y_1)=(3, - 1)\) and \((x_2,y_2)=(4,7)\). So \(m=\frac{7-(-1)}{4 - 3}=\frac{7 + 1}{1}=8\).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((3,-1)\) and \(m = 8\). Substitute these values into the formula: \(y-(-1)=8(x - 3)\). Simplify this equation: \(y + 1=8x-24\). Then, subtract 1 from both sides to get \(y = 8x-25\).

Answer:

\(8x - 25\)