Question

1. $y = -3x + 6$ $m=-3$, $b = 6$ $(0,6)$

Explanation:

Step1: Identify y - intercept

The equation is in slope - intercept form $y = mx + b$, where $b$ is the y - intercept. Here $b = 6$, so the line crosses the y - axis at the point $(0,6)$. Plot this point on the graph.

Step2: Identify slope

The slope $m=-3=\frac{-3}{1}$. From the y - intercept $(0,6)$, use the slope to find another point. The slope formula is $m=\frac{\Delta y}{\Delta x}$. Starting from $(0,6)$, move 1 unit to the right (increase $x$ by 1) and 3 units down (decrease $y$ by 3) to get the point $(1,3)$.

Step3: Draw the line

Connect the two points $(0,6)$ and $(1,3)$ with a straight line. This line represents the graph of the equation $y=-3x + 6$.

Answer:

The graph of the line $y=-3x + 6$ is drawn by first plotting the y - intercept $(0,6)$ and then using the slope to find another point $(1,3)$ and connecting them.