Question

1. short answer for the equation y = 2x - 5, explain how the graph moves starting from a point.

Explanation:

The equation $y=2x-5$ is in slope-intercept form $y=mx+b$, where $m=2$ (slope) and $b=-5$ (y-intercept). Starting from any point $(x_1, y_1)$ on the line:

1. The slope $2 = \frac{2}{1}$ means for every 1 unit increase in the $x$-value (move right 1), the $y$-value increases by 2 units (move up 2).
2. Conversely, for every 1 unit decrease in the $x$-value (move left 1), the $y$-value decreases by 2 units (move down 2).

The line can also be traced by starting at the y-intercept $(0, -5)$ and using the slope to plot additional points.

Answer:

Starting from any point on the graph of $y=2x-5$, for each 1-unit horizontal shift right, the graph shifts 2 units up; for each 1-unit horizontal shift left, the graph shifts 2 units down. This movement is defined by the slope of 2, and the line crosses the y-axis at $(0, -5)$.