Question

do you know how?

1. chrissie says the equation of the line shown on the graph is $y = \frac{1}{2}x - 5$. george says that the equation of the line is $y = -\frac{1}{2}x + 5$. which student is correct? explain.

Explanation:

Step1: Identify slope and y-intercept

The line crosses the y - axis at (0, 5), so the y - intercept \(b = 5\). To find the slope, use two points, e.g., (0, 5) and (6, 2). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting values: \(m=\frac{2 - 5}{6 - 0}=\frac{-3}{6}=-\frac{1}{2}\).

Step2: Write the equation

The slope - intercept form is \(y = mx + b\). With \(m = -\frac{1}{2}\) and \(b = 5\), the equation is \(y=-\frac{1}{2}x + 5\), which matches George's equation. Chrissie's equation has a positive slope (\(\frac{1}{2}\)) and y - intercept - 5, which doesn't match the graph.

Answer:

George is correct. The line has a y - intercept of 5 (crosses y - axis at (0, 5)) and a negative slope (\(m = -\frac{1}{2}\)) calculated from points like (0, 5) and (6, 2). The equation \(y = -\frac{1}{2}x+5\) (George's) matches, while Chrissie's has a positive slope and wrong y - intercept.