Give The Slope And The \[$ Y \$\]-intercept Of The Line With The Given Equation. Then, Graph The Linear Equation.Equation: $ Y = 3x + 7 $What Is The Slope? Select The Correct Choice And Fill In Any Answer Boxes Within Your Choice.A.
Understanding the Equation
The given equation is in the form of a linear equation, which is represented as y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation is y = 3x + 7. To find the slope and y-intercept, we need to identify the values of m and b.
Finding the Slope
The slope of a linear equation is the coefficient of the x-term. In this case, the coefficient of x is 3. Therefore, the slope of the line is 3.
Finding the y-Intercept
The y-intercept of a linear equation is the value of y when x is equal to 0. In this case, when x is equal to 0, y is equal to 7. Therefore, the y-intercept of the line is 7.
Graphing the Linear Equation
To graph the linear equation, we need to plot two points on the coordinate plane. We can use the slope and y-intercept to find the coordinates of these points.
Step 1: Plot the y-Intercept
The y-intercept is the point where the line intersects the y-axis. In this case, the y-intercept is (0, 7). We can plot this point on the coordinate plane.
Step 2: Use the Slope to Find the Second Point
The slope of the line is 3, which means that for every 1 unit we move to the right, we move up 3 units. We can use this information to find the coordinates of the second point.
Let's say we move 1 unit to the right from the y-intercept. The new x-coordinate is 1. To find the new y-coordinate, we multiply the slope by the change in x and add it to the y-intercept.
y = 3(1) + 7 y = 3 + 7 y = 10
So, the coordinates of the second point are (1, 10).
Step 3: Plot the Second Point
We can plot the second point on the coordinate plane.
Step 4: Draw the Line
Now that we have two points on the coordinate plane, we can draw the line that passes through these points.
Conclusion
In this article, we learned how to find the slope and y-intercept of a linear equation. We also learned how to graph the linear equation using the slope and y-intercept. The slope of the line is 3, and the y-intercept is 7. We plotted two points on the coordinate plane and drew the line that passes through these points.
Key Takeaways
- The slope of a linear equation is the coefficient of the x-term.
- The y-intercept of a linear equation is the value of y when x is equal to 0.
- To graph a linear equation, we need to plot two points on the coordinate plane and draw the line that passes through these points.
Frequently Asked Questions
Q: What is the slope of the line y = 3x + 7?
A: The slope of the line is 3.
Q: What is the y-intercept of the line y = 3x + 7?
A: The y-intercept of the line is 7.
Q: How do I graph a linear equation?
A: To graph a linear equation, you need to plot two points on the coordinate plane and draw the line that passes through these points.
Q: What are the coordinates of the y-intercept?
A: The coordinates of the y-intercept are (0, 7).
Q: What are the coordinates of the second point?
A: The coordinates of the second point are (1, 10).
Q: How do I find the coordinates of the second point?
A: To find the coordinates of the second point, you need to multiply the slope by the change in x and add it to the y-intercept.
Q: What is the equation of the line?
Frequently Asked Questions
Q: What is the slope of the line y = 3x + 7?
A: The slope of the line is 3. The slope is the coefficient of the x-term in the linear equation.
Q: What is the y-intercept of the line y = 3x + 7?
A: The y-intercept of the line is 7. The y-intercept is the value of y when x is equal to 0.
Q: How do I graph a linear equation?
A: To graph a linear equation, you need to plot two points on the coordinate plane and draw the line that passes through these points. You can use the slope and y-intercept to find the coordinates of the points.
Q: What are the coordinates of the y-intercept?
A: The coordinates of the y-intercept are (0, 7). The y-intercept is the point where the line intersects the y-axis.
Q: What are the coordinates of the second point?
A: The coordinates of the second point are (1, 10). You can find the coordinates of the second point by multiplying the slope by the change in x and adding it to the y-intercept.
Q: How do I find the coordinates of the second point?
A: To find the coordinates of the second point, you need to multiply the slope by the change in x and add it to the y-intercept. For example, if the slope is 3 and the change in x is 1, the new y-coordinate is 3(1) + 7 = 10.
Q: What is the equation of the line?
A: The equation of the line is y = 3x + 7. This is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Q: How do I determine the slope and y-intercept of a linear equation?
A: To determine the slope and y-intercept of a linear equation, you need to identify the values of m and b in the equation y = mx + b. The slope is the coefficient of the x-term, and the y-intercept is the value of y when x is equal to 0.
Q: Can I have a negative slope?
A: Yes, you can have a negative slope. A negative slope means that the line slopes downward from left to right.
Q: Can I have a zero slope?
A: Yes, you can have a zero slope. A zero slope means that the line is horizontal and does not slope upward or downward.
Q: Can I have a vertical line?
A: Yes, you can have a vertical line. A vertical line has an undefined slope, as it does not slope upward or downward.
Q: How do I graph a vertical line?
A: To graph a vertical line, you need to plot a single point on the coordinate plane and draw a vertical line through that point. The equation of a vertical line is x = a, where a is the x-coordinate of the point.
Q: How do I graph a horizontal line?
A: To graph a horizontal line, you need to plot a single point on the coordinate plane and draw a horizontal line through that point. The equation of a horizontal line is y = b, where b is the y-coordinate of the point.
Q: Can I have a line with a slope of 0 and a y-intercept of 0?
A: No, you cannot have a line with a slope of 0 and a y-intercept of 0. If the slope is 0, the line is horizontal and does not slope upward or downward. If the y-intercept is 0, the line passes through the origin (0, 0) and does not intersect the y-axis.
Q: Can I have a line with a slope of 1 and a y-intercept of 1?
A: Yes, you can have a line with a slope of 1 and a y-intercept of 1. The equation of this line is y = x + 1.
Q: Can I have a line with a slope of -1 and a y-intercept of 1?
A: Yes, you can have a line with a slope of -1 and a y-intercept of 1. The equation of this line is y = -x + 1.
Q: Can I have a line with a slope of 2 and a y-intercept of 3?
A: Yes, you can have a line with a slope of 2 and a y-intercept of 3. The equation of this line is y = 2x + 3.
Q: Can I have a line with a slope of -2 and a y-intercept of 3?
A: Yes, you can have a line with a slope of -2 and a y-intercept of 3. The equation of this line is y = -2x + 3.
Q: Can I have a line with a slope of 3 and a y-intercept of -2?
A: Yes, you can have a line with a slope of 3 and a y-intercept of -2. The equation of this line is y = 3x - 2.
Q: Can I have a line with a slope of -3 and a y-intercept of -2?
A: Yes, you can have a line with a slope of -3 and a y-intercept of -2. The equation of this line is y = -3x - 2.
Q: Can I have a line with a slope of 4 and a y-intercept of -3?
A: Yes, you can have a line with a slope of 4 and a y-intercept of -3. The equation of this line is y = 4x - 3.
Q: Can I have a line with a slope of -4 and a y-intercept of -3?
A: Yes, you can have a line with a slope of -4 and a y-intercept of -3. The equation of this line is y = -4x - 3.
Q: Can I have a line with a slope of 5 and a y-intercept of -4?
A: Yes, you can have a line with a slope of 5 and a y-intercept of -4. The equation of this line is y = 5x - 4.
Q: Can I have a line with a slope of -5 and a y-intercept of -4?
A: Yes, you can have a line with a slope of -5 and a y-intercept of -4. The equation of this line is y = -5x - 4.
Q: Can I have a line with a slope of 6 and a y-intercept of -5?
A: Yes, you can have a line with a slope of 6 and a y-intercept of -5. The equation of this line is y = 6x - 5.
Q: Can I have a line with a slope of -6 and a y-intercept of -5?
A: Yes, you can have a line with a slope of -6 and a y-intercept of -5. The equation of this line is y = -6x - 5.
Q: Can I have a line with a slope of 7 and a y-intercept of -6?
A: Yes, you can have a line with a slope of 7 and a y-intercept of -6. The equation of this line is y = 7x - 6.
Q: Can I have a line with a slope of -7 and a y-intercept of -6?
A: Yes, you can have a line with a slope of -7 and a y-intercept of -6. The equation of this line is y = -7x - 6.
Q: Can I have a line with a slope of 8 and a y-intercept of -7?
A: Yes, you can have a line with a slope of 8 and a y-intercept of -7. The equation of this line is y = 8x - 7.
Q: Can I have a line with a slope of -8 and a y-intercept of -7?
A: Yes, you can have a line with a slope of -8 and a y-intercept of -7. The equation of this line is y = -8x - 7.
Q: Can I have a line with a slope of 9 and a y-intercept of -8?
A: Yes, you can have a line with a slope of 9 and a y-intercept of -8. The equation of this line is y = 9x - 8.
Q: Can I have a line with a slope of -9 and a y-intercept of -8?
A: Yes, you can have a line with a slope of -9 and a y-intercept of -8. The equation of this line is y = -9x - 8.
Q: Can I have a line with a slope of 10 and a y-intercept of -9?
A: Yes, you can have a line with a slope of 10 and a y-intercept of -9. The equation of this line is y = 10x - 9.
Q: Can I have a line with a slope of -10 and a y-intercept of -9?
A: Yes, you can have a line with a slope of -10 and a y-intercept of -9. The equation of this line is y = -