Question

find an equation of the line described below. write the equation in slope-intercept form (solved for y) when possible.
through (8,3) and (0,0)

the equation is \boxed{}.
(simplify your answer. type your answer in slope-intercept form. use integers or fractions for any numbers in the equation.)

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, \((x_1, y_1)=(0,0)\) and \((x_2, y_2)=(8,3)\). So, \( m=\frac{3 - 0}{8 - 0}=\frac{3}{8} \).

Step2: Determine the y-intercept

The slope - intercept form of a line is \( y = mx + b \), where \( b \) is the y - intercept. Since the line passes through \((0,0)\), when \( x = 0 \), \( y = 0 \). Substituting \( x = 0 \), \( y = 0 \) and \( m=\frac{3}{8} \) into \( y=mx + b \), we get \( 0=\frac{3}{8}(0)+b \), so \( b = 0 \).

Step3: Write the equation

Substituting \( m=\frac{3}{8} \) and \( b = 0 \) into the slope - intercept form \( y=mx + b \), we get \( y=\frac{3}{8}x+0 \), which simplifies to \( y=\frac{3}{8}x \).

Answer:

\( y=\frac{3}{8}x \)