Identify the slope and the y-intercept of the equation, then graph the equation: y=2x+1
Slope(m) =
y-intercept(b)=
The slope (m) of the equation y=2x+1 is 2.
The y-intercept (b) of the equation y=2x+1 is 1.
To graph the equation, start by plotting the y-intercept, which is the point (0,1). Then, use the slope to find another point on the line. The slope of 2 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 2. So, starting from the y-intercept (0,1), we can go up 2 units and right 1 unit to find another point (1,3).
Now, draw a straight line passing through the two points (0,1) and (1,3) to complete the graph.
Explain how rise over run is relating to change in y over change in x?
Rise over run is a way to describe the slope of a line. It represents the change in the y-coordinate divided by the change in the x-coordinate between two points on the line.
When we say "rise over run," the "rise" refers to the change in the y-coordinate, and the "run" refers to the change in the x-coordinate.
So, in the equation y = mx + b, where m represents the slope, rise over run can be calculated as:
Rise/Run = (change in y-coordinate) / (change in x-coordinate) = (y₂ - y₁) / (x₂ - x₁)
This concept helps us understand how the y-coordinate changes in relation to the x-coordinate as we move from one point to another on the line. It tells us how much the y-value changes for each unit change in the x-value.
In the equation y = 2x + 1, the slope is 2, and we can see that for every increase of 1 unit in the x-coordinate, there is a corresponding increase of 2 units in the y-coordinate. So, the rise over run in this case is 2/1, which represents the change in y over the change in x.
In the equation y=2x+1, the slope (m) is 2 and the y-intercept (b) is 1.
To graph the equation, you can start by plotting the y-intercept, which is the point (0, 1). This represents the point where the line intersects the y-axis.
Next, you can use the slope to find other points on the line. Since the slope is 2, it means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by 2. Similarly, for every decrease of 1 in the x-coordinate, the y-coordinate will decrease by 2.
Using this information, you can plot additional points on the graph. For example, if you increase the x-coordinate by 1 from the y-intercept (0, 1), you will get the point (1, 3). If you increase it by another 1, you will get (2, 5), and so on. Similarly, if you decrease the x-coordinate by 1 from the y-intercept, you will get (-1, -1), and if you decrease it by another 1, you will get (-2, -3).
Once you have plotted enough points, you can connect them with a straight line to graph the equation y=2x+1.