Question

1. find the equation of the line that contains the given points. write the equation in slope - intercept form, if possible. (0,16) and (-4,0)

select the correct choice below and, if necessary, fill in the answer box to complete your choice. (simplify your answer. use integers or fractions for any numbers in the equation.)
a. the equation of the line cannot be written in slope - intercept form. the equation of the line is

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(0,16)\) and \((x_2, y_2)=(-4,0)\). So, \( m=\frac{0 - 16}{-4 - 0}=\frac{-16}{-4}=4 \).

Step2: Determine the y - intercept

The slope - intercept form of a line is \( y = mx + b \), where \( b \) is the y - intercept. We know that the line passes through the point \((0,16)\). When \( x = 0 \), \( y=b \). So, \( b = 16 \).

Step3: Write the equation

Substitute \( m = 4 \) and \( b = 16 \) into the slope - intercept form \( y=mx + b \). We get \( y = 4x+16 \).

Answer:

\( y = 4x + 16 \)