Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
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.
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.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.