Question

1. $y = x + 5$

Explanation:

Step1: Identify slope and y-intercept

The equation $y = x + 5$ is in slope-intercept form $y=mx+b$, where $m=1$ (slope) and $b=5$ (y-intercept, the point $(0,5)$).

Step2: Plot the y-intercept

Mark the point $(0, 5)$ on the coordinate grid, where $x=0$ and $y=5$.

Step3: Use slope to find a second point

Since slope $m=\frac{\text{rise}}{\text{run}} = \frac{1}{1}$, from $(0,5)$, move 1 unit up and 1 unit right to get the point $(1, 6)$. Alternatively, move 1 unit down and 1 unit left to get $(-1, 4)$.

Step4: Draw the line

Connect the plotted points with a straight line, extending it across the entire grid.

Answer:

The graph of $y = x + 5$ is a straight line passing through points such as $(0,5)$, $(1,6)$, and $(-1,4)$, with a slope of 1 and y-intercept at $(0,5)$.