Question

write the equation of a line in slope intercept form given the points (5, 4) and (6, 7).

Explanation:

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 \((5, 4)\) and \((6, 7)\), we have \(x_1 = 5\), \(y_1 = 4\), \(x_2 = 6\), \(y_2 = 7\). So \(m=\frac{7 - 4}{6 - 5}=\frac{3}{1}=3\).

Step2: Find the y - intercept ($b$)

Use the slope - intercept form \(y=mx + b\) and one of the points (let's use \((5,4)\)) and \(m = 3\). Substitute \(x = 5\), \(y = 4\) and \(m = 3\) into \(y=mx + b\): \(4=3\times5 + b\). Simplify the right - hand side: \(4 = 15 + b\). Then solve for \(b\): \(b=4 - 15=- 11\).

Step3: Write the equation

Now that we have \(m = 3\) and \(b=-11\), the slope - intercept form of the line is \(y=3x-11\).

Answer:

$y = 3x - 11$