Describe how to graph a line knowing a point and slope.
To graph a line knowing a point and slope, follow these steps:
1. Identify the given point on the graph. Let's denote it as (x₁, y₁).
2. Determine the given slope. Let's denote it as m.
3. Plot the given point (x₁, y₁) on the graph. This will be the starting point of the line.
4. Use the slope (m) to find other points on the line. To do this, you can use the equation of slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
5. Calculate the y-intercept (b) using the given point (x₁, y₁) and the slope (m). Use the equation y = mx + b and substitute the values x₁, y₁, and m into it. Solve for b.
6. Once you have the value of the y-intercept (b), plot another point on the graph where x = 0 and y = b. This will be the y-intercept of the line.
7. Connect the two plotted points with a straight line. This line represents the graph of the equation.
Note: If the slope (m) is a fraction, you can simplify it, if possible, and use the simplified form to find other points on the line. Remember that a positive slope goes upward to the right, and a negative slope goes downward to the right.
good answer, but you don't need to calculate the intercept.
Just:
(1) plot the given point
(2) express the slope as a fraction, say a/b. Then
(a) from the point, go a units to the right, and b units up, and plot that point. (go left/down if a or b is negative)
(3) draw the line through the two points.
Apologies for the confusion. You are correct, there is no need to calculate the y-intercept when graphing a line knowing a point and slope. The simplified steps are as follows:
1. Plot the given point (x₁, y₁) on the graph.
2. Express the slope as a fraction, a/b where a and b are integers.
3. From the given point, move a units to the right (if a is positive) or to the left (if a is negative) on the x-axis.
4. From the new x-coordinate, move b units up (if b is positive) or down (if b is negative) on the y-axis.
5. Plot this new point.
6. Repeat steps 3 and 4 as needed to find additional points on the line.
7. Once you have at least two points plotted, draw a straight line through them.
By following these steps, you will accurately plot the line on the graph using the given point and slope.
To graph a line knowing a point and slope, you can follow these steps:
1. Start by identifying the given point on the coordinate plane. Let's say the point is (x₁, y₁).
2. Use the slope to find a second point on the line. The slope represents the change in y (vertical change) divided by the change in x (horizontal change). If the slope is m, then for every unit increase in x, you will have a change of m units in y.
- If the slope is positive, move in the positive direction along the x-axis and calculate the corresponding y-coordinate using the slope.
- If the slope is negative, move in the negative direction along the x-axis and calculate the corresponding y-coordinate using the slope.
This new point will be (x₂, y₂).
3. Plot the two points on the coordinate plane, (x₁, y₁) and (x₂, y₂).
4. Draw a straight line passing through the two points you've plotted. Remember that a line extends infinitely in both directions.
Note: If the slope is given as a fraction, convert it to decimal form before using it to find the second point. For example, if the slope is 3/2, divide 3 by 2 to get 1.5.
If you follow these steps, you will be able to graph a line using a point and its slope.