Question

graph this line using the slope and y-intercept: y = x - 10 click to select points on the graph.

Explanation:

Step1: Identify slope and y - intercept

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the equation $y=x - 10$, we can rewrite it as $y = 1x+( - 10)$. So, the slope $m = 1$ (which can be thought of as $\frac{1}{1}$, meaning for every 1 unit we move to the right along the x - axis, we move up 1 unit along the y - axis) and the y - intercept $b=- 10$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-10$. So we plot the point $(0,-10)$ on the graph.

Step3: Use the slope to find another point

Since the slope $m = 1=\frac{\text{rise}}{\text{run}}=\frac{1}{1}$, starting from the point $(0,-10)$, we move 1 unit to the right (increase $x$ by 1) and 1 unit up (increase $y$ by 1). So we get the point $(0 + 1,-10 + 1)=(1,-9)$. We can also move in the opposite direction: from $(0,-10)$, move 1 unit to the left (decrease $x$ by 1) and 1 unit down (decrease $y$ by 1) to get the point $(-1,-11)$. We can continue this process to get more points, but with two points $(0,-10)$ and $(1,-9)$ (or any other two points found using the slope), we can draw the line.

Answer:

To graph the line $y=x - 10$:

1. Plot the y - intercept at the point $(0,-10)$.
2. Use the slope of 1 (rise 1, run 1) to find another point (e.g., from $(0,-10)$, moving right 1 and up 1 gives $(1,-9)$).
3. Draw a straight line through the plotted points.