Sure, let's break down how to graph the line represented by the equation [tex]\( y = -\frac{2}{3}x + 1 \)[/tex] using clear steps:
1. Identify the slope and y-intercept:
- The equation is in 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]\( m = -\frac{2}{3} \)[/tex] and the y-intercept [tex]\( b = 1 \)[/tex].
2. Plot the y-intercept:
- The y-intercept is the point where the line crosses the y-axis.
- For this equation, the y-intercept is 1. So, plot a point at (0, 1) on the graph.
3. Use the slope to find another point:
- The slope of the line is [tex]\( -\frac{2}{3} \)[/tex]. This means for every 3 units you move to the right along the x-axis, you move 2 units down along the y-axis (because the slope is negative).
- Starting from the y-intercept point (0, 1), move 3 units to the right (to x = 3) and then 2 units down. This brings you to the point (3, -1). Plot this point.
4. Draw the line:
- Draw a straight line through the two points (0, 1) and (3, -1). Extend the line in both directions and make sure it passes through these points accurately.
The graph of the line [tex]\( y = -\frac{2}{3}x + 1 \)[/tex] will have these characteristics. Steps are the same whether using graph paper or a digital drawing tool.
