Question

what is the y-intercept of the line that passes through points (6,7) and (3,3)? type your answer in the boxes

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

Step2: Use point - slope form to find the equation of the line

The point - slope form is \(y - y_1=m(x - x_1)\). Let's use the point \((3,3)\). Substitute \(m = \frac{4}{3}\), \(x_1 = 3\), \(y_1 = 3\) into the formula: \(y - 3=\frac{4}{3}(x - 3)\).

Step3: Simplify the equation to slope - intercept form (\(y=mx + b\))

Expand the right - hand side: \(y - 3=\frac{4}{3}x-4\). Then add 3 to both sides: \(y=\frac{4}{3}x-4 + 3=\frac{4}{3}x-1\). In the slope - intercept form \(y = mx + b\), \(b\) is the y - intercept.

Answer:

-1