Question

graph the following features: • y-intercept = 1 • slope = -3

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the y - intercept $b = 1$ and the slope $m=- 3$, the equation of the line is $y=-3x + 1$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=1$. So we plot the point $(0,1)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m=\frac{\text{rise}}{\text{run}}=-3=\frac{- 3}{1}$. Starting from the y - intercept $(0,1)$, we move down 3 units (because the rise is - 3) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,1-3)=(1, - 2)$. We can also move up 3 units and left 1 unit from the y - intercept: $(0-1,1 + 3)=(-1,4)$.

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., $(0,1)$ and $(1,-2)$ or $(0,1)$ and $(-1,4)$) to represent the linear equation $y=-3x + 1$.

Answer:

To graph the line with y - intercept 1 and slope - 3:

1. Plot the point \((0,1)\) (the y - intercept).
2. Use the slope \(-3=\frac{-3}{1}\): from \((0,1)\), move 3 units down and 1 unit right to get \((1, - 2)\) (or 3 units up and 1 unit left to get \((-1,4)\)).
3. Draw a straight line through these points. The equation of the line is \(y=-3x + 1\).