Question

writing an equation given two points partner worksheet each partner writes the equation of the line that passes through the two given points they should put their equation in slope - intercept form (y = mx + b) partners a and b then compare their answers the answers should be the same even though the problems are different if the answers dont match, work together to determine any mistakes partner a 1. (1,5) and (3,11) 2. (-5,-12) and (8,1) 3. (-3,-3) and (3,1) 4. (-1,6) and (4,-4) 5. (-6,2) and (-2,0) 6. (-2,-3) and (4,6)

Explanation:

Step1: Find 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 the points \((1, 5)\) and \((3, 11)\), we have \(x_1 = 1\), \(y_1 = 5\), \(x_2 = 3\), \(y_2 = 11\). So \(m=\frac{11 - 5}{3 - 1}=\frac{6}{2}=3\).

Step2: Find the y - intercept (b)

We use the slope - intercept form \(y = mx + b\) and substitute one of the points (let's use \((1, 5)\)) and \(m = 3\). So \(5=3\times1 + b\). Solving for \(b\), we get \(b=5 - 3=2\).

Step3: Write the equation

Using \(m = 3\) and \(b = 2\) in the slope - intercept form \(y=mx + b\), the equation is \(y = 3x+2\).

Answer:

For the points \((1,5)\) and \((3,11)\), the equation of the line in slope - intercept form is \(y = 3x + 2\)