To determine the graph of the equation [tex]\( y = -3x - 1 \)[/tex], follow these steps:
1. Identify the slope and y-intercept:
- The equation [tex]\( y = -3x - 1 \)[/tex] is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- Here, the slope [tex]\( m \)[/tex] is [tex]\(-3\)[/tex], and the y-intercept [tex]\( b \)[/tex] is [tex]\(-1\)[/tex].
2. Plot the y-intercept:
- The y-intercept is the point where the line crosses the y-axis. For [tex]\( y = -3x - 1 \)[/tex], this occurs at [tex]\((0, -1)\)[/tex]. Plot the point [tex]\((0, -1)\)[/tex] on the graph.
3. Use the slope to find another point:
- The slope [tex]\( m = -3 \)[/tex] means that for each increase of 1 unit in [tex]\( x \)[/tex], [tex]\( y \)[/tex] decreases by 3 units.
- Starting from the y-intercept [tex]\((0, -1)\)[/tex], move 1 unit to the right (increase [tex]\( x \)[/tex] by 1) and then move 3 units down (decrease [tex]\( y \)[/tex] by 3).
- This gives the point [tex]\((1, -4)\)[/tex]. Plot the point [tex]\((1, -4)\)[/tex] on the graph.
4. Find another point (optional, to double-check accuracy):
- To ensure the line is accurate, use another value for [tex]\( x \)[/tex] and solve for [tex]\( y \)[/tex]:
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -3(-1) - 1 = 3 - 1 = 2
\][/tex]
- This gives the point [tex]\((-1, 2)\)[/tex]. Plot the point [tex]\((-1, 2)\)[/tex] on the graph.
5. Draw the line:
- With points [tex]\((0, -1)\)[/tex], [tex]\((1, -4)\)[/tex], and [tex]\((-1, 2)\)[/tex] plotted on the graph, draw a straight line through these points.
The line you draw will represent the graph of the equation [tex]\( y = -3x - 1 \)[/tex], and it should have a downward slope, starting at [tex]\((0, -1)\)[/tex] on the y-axis and passing through points [tex]\((1, -4)\)[/tex] and [tex]\((-1, 2)\)[/tex].
