Question

determine the equation of the line that passes through the given points. (if you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)(2, 6) and (4, 16)a. $y = -4x + 5$b. $y = 5x - 16$c. $y = 5x - 4$d. $y = -5x + 4$please select the best answer from the choices provideda\\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 \( (2,6) \) and \( (4,16) \), we have \( x_1 = 2,y_1 = 6,x_2=4,y_2 = 16 \). So \( m=\frac{16 - 6}{4 - 2}=\frac{10}{2}=5 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \( (2,6) \) and \( m = 5 \), we get \( y-6 = 5(x - 2) \).

Step3: Simplify the equation

Expand the right - hand side: \( y-6=5x-10 \). Then add 6 to both sides: \( y=5x-10 + 6=5x-4 \). We can also check by substituting the points into the equation. For \( (2,6) \): \( y=5\times2-4=10 - 4 = 6 \) (satisfied). For \( (4,16) \): \( y=5\times4-4=20 - 4 = 16 \) (satisfied).

Answer:

C. \( y = 5x - 4 \)