Graph the line with the given point and slope.
Through (0,3); slope=-1/2
To graph a line given a point and slope, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope.
In this case, the given point is (0, 3) and the slope is -1/2. We can substitute these values into the point-slope form to get:
y - 3 = -1/2(x - 0)
Simplifying this equation, we have:
y - 3 = -1/2x
To graph this line, we can first plot the given point (0, 3) on the graph. Then, using the slope -1/2, we can find another point on the line.
From the point (0,3), we can go "down 1 and to the right 2" to find the next point.
So, starting from (0,3), we can move down 1 unit and right 2 units to get the point (2, 2).
Now, we can connect these two points with a straight line to graph the line.
The graph of the line through (0, 3) with a slope of -1/2 is a downward-sloping line that passes through the points (0, 3) and (2, 2).
To graph the line with the given point and slope, we need to use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where:
- m is the slope of the line
- b is the y-intercept of the line
In this case, the slope is -1/2, and the given point is (0, 3).
We can substitute these values into the equation to find the y-intercept (b):
3 = (-1/2)(0) + b
3 = 0 + b
b = 3
Now we have the equation of the line:
y = (-1/2)x + 3
To graph the line, we can plot the given point (0, 3), and then use the slope to find additional points. The slope tells us that for every 2 units we move to the left (in the x-direction), we need to move 1 unit down (in the y-direction).
Starting from the point (0, 3), we can go 2 units to the left and 1 unit down, giving us the point (-2, 2). Similarly, we can go 2 units to the right and 1 unit up, giving us the point (2, 4).
Plotting these points, we can draw a straight line passing through all three points: (0, 3), (-2, 2), and (2, 4).
The graph of the line is as follows:
To graph a line using a point and a slope, you can follow these steps:
1. Start by plotting the given point on the coordinate plane. In this case, the point is (0, 3). This means the line will pass through the y-axis at 3.
2. Use the slope to find additional points on the line. The slope is given as -1/2. The slope represents the ratio of the vertical change (rise) to the horizontal change (run).
- Since the slope is negative, we can interpret it as a negative slope. This means that the line will decrease as you move from left to right.
- The numerator of the slope -1/2 represents the vertical change or the change in y-coordinates, which is -1. This means for every unit you move to the right, the line will go down by 1 unit.
- The denominator of the slope -1/2 represents the horizontal change or the change in x-coordinates, which is 2. This means for every 2 units you move to the right, the line will go down by 1 unit.
3. Starting from the point (0, 3), apply the vertical and horizontal changes to find additional points on the line.
- To move to the right by 2 units, add 2 to the x-coordinate of the point (0, 3), giving us the point (2, 3 - 1) = (2, 2).
4. Plot the additional point (2, 2) on the coordinate plane.
5. Draw a straight line passing through the given point (0, 3) and the additional point (2, 2).
By following these steps, you should have successfully graphed the line passing through the point (0, 3) with a slope of -1/2.