Question

find the equation of the line specified. the line passes through the points (5, 2) and (6, 4) a. y = 2x - 8 c. y = 2x + 12 b. y = 4x - 8 d. y = 2x + 2 please select the best answer from the choices provided a b c d

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \((5, 2)\) and \((6, 4)\), we have \( x_1 = 5,y_1 = 2,x_2=6,y_2 = 4 \). So \( m=\frac{4 - 2}{6 - 5}=\frac{2}{1}=2 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((5, 2)\) and \( m = 2 \), we get \( y-2 = 2(x - 5) \).

Step3: Simplify the equation

Expand the right - hand side: \( y-2=2x-10 \). Then add 2 to both sides: \( y=2x - 8 \). We can also check by plugging in the points. For \( x = 5 \), \( y=2\times5-8 = 10 - 8=2 \) (matches the point \((5,2)\)). For \( x = 6 \), \( y=2\times6-8=12 - 8 = 4 \) (matches the point \((6,4)\)).

Answer:

A. \( y = 2x-8 \)