Question

1. find the equation of the line that passes through the points (2, 6) and (-2, 4)?

1. find the equation of a line that passes through the points (2, 16) and (-1, 7).

1. find the equation of a line that passes through the points (2,13) and (1,8)

1. find the equation of a line that passes through the points (4, 3) and (8,1)

challenge questions

1. find the equation of a line that passes through the points (2, 5) and (2, 12).

1. find the equation of a line that passes through the points (5, 3) and (2, 3).

Explanation:

Question 6

Step1: Calculate the slope $m$

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \((2, 6)\) and \((-2, 4)\), we have \(x_1 = 2\), \(y_1 = 6\), \(x_2=-2\), \(y_2 = 4\). So \(m=\frac{4 - 6}{-2 - 2}=\frac{-2}{-4}=\frac{1}{2}\).

Step2: Use point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((2, 6)\) and \(m=\frac{1}{2}\), we get \(y - 6=\frac{1}{2}(x - 2)\).

Step3: Simplify to slope - intercept form

\(y-6=\frac{1}{2}x - 1\), then \(y=\frac{1}{2}x+5\).

Step1: Calculate the slope \(m\)

For points \((2, 16)\) and \((-1, 7)\), using \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \(x_1 = 2\), \(y_1 = 16\), \(x_2=-1\), \(y_2 = 7\). So \(m=\frac{7 - 16}{-1 - 2}=\frac{-9}{-3}=3\).

Step2: Use point - slope form

Using the point \((2, 16)\) and \(m = 3\), \(y-16=3(x - 2)\).

Step3: Simplify

\(y-16 = 3x-6\), then \(y=3x + 10\).

Step1: Calculate the slope \(m\)

For points \((2, 13)\) and \((1, 8)\), using \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \(x_1 = 2\), \(y_1 = 13\), \(x_2 = 1\), \(y_2 = 8\). So \(m=\frac{8 - 13}{1 - 2}=\frac{-5}{-1}=5\).

Step2: Use point - slope form

Using the point \((1, 8)\) and \(m = 5\), \(y - 8=5(x - 1)\).

Step3: Simplify

\(y-8=5x - 5\), then \(y=5x + 3\).

Answer:

\(y = \frac{1}{2}x + 5\)

Question 7