Question

find the equation of the line specified.
the line passes through the points ( 5, 2) and ( 6, 4)
a. y = 2x - 8
b. y = 4x - 8
c. y = 2x + 12
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 the 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 to find the equation

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: \( y=2x - 10 + 2=2x-8 \). We can also check by substituting the points into the equation. For \((5,2)\): Left - hand side \( y = 2 \), Right - hand side \( 2\times5-8 = 10 - 8 = 2 \). For \((6,4)\): Left - hand side \( y = 4 \), Right - hand side \( 2\times6-8=12 - 8 = 4 \).

Answer:

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