Question

of each line defined below and compare their values. equation of line a: $y + 1=\frac{1}{2}(x - 4)$ graph of line b:

Explanation:

Step1: Rewrite line A in slope - intercept form

Starting with $y + 1=\frac{1}{2}(x - 4)$, distribute the $\frac{1}{2}$: $y+1=\frac{1}{2}x-2$. Then subtract 1 from both sides to get $y=\frac{1}{2}x - 3$. The slope of line A is $\frac{1}{2}$ and the y - intercept is - 3.

Step2: Determine slope of line B from graph

To find the slope of line B from the graph, we can use two points on the line. Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$ on line B. If we take two distinct points on the line and use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we find that the slope of line B is also $\frac{1}{2}$ (by counting the rise over run, for example, if we move 2 units to the right and 1 unit up between two points on the line).

Since the slopes of line A and line B are equal, the lines are parallel (assuming they are not the same line, which we can tell from the y - intercepts if we could fully determine the equation of line B from the graph).

Answer:

The slopes of line A and line B are equal.