Question

a line passes through the points (1, 1) and (2, 8). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(1, 1)\) and \((x_2, y_2)=(2, 8)\). So, \( m=\frac{8 - 1}{2 - 1}=\frac{7}{1} = 7 \).

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 \((1, 1)\) and \( m = 7 \), we have \( y - 1=7(x - 1) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 1=7x-7 \). Then, add 1 to both sides to get \( y=7x-7 + 1 \), which simplifies to \( y = 7x-6 \).

Answer:

\( y = 7x-6 \)