Identify the slope and the y-intercept of the equation, then graph the equation:
y=2/3x + 5
Slope(m) =
y-intercept(b)=
Slope (m) = 2/3
y-intercept (b) = 5
To graph the equation, we can start by plotting the y-intercept, which is the point (0,5). From that point, we can use the slope to find other points.
To find the next point, we can use the slope-intercept form of the equation, which states that y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation is y = (2/3)x + 5.
To find the x-coordinate of the next point, we can simply move 3 units to the right, since the slope is 2/3. So the next x-coordinate is 3.
Plugging this x-coordinate into the equation, we get y = (2/3)(3) + 5 = 2 + 5 = 7. So the next point is (3,7).
We can repeat this process to find more points.
x = 0: y = (2/3)(0) + 5 = 0 + 5 = 5. So the point is (0,5).
x = 3: y = (2/3)(3) + 5 = 2 + 5 = 7. So the point is (3,7).
x = 6: y = (2/3)(6) + 5 = 4 + 5 = 9. So the point is (6,9).
Plotting these points and connecting them with a line, we get the graph of the equation y = (2/3)x + 5.
To identify the slope and the y-intercept of the equation y = (2/3)x + 5, we can see that the equation is already in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
So, the slope (m) of the equation is 2/3.
The y-intercept (b) of the equation is 5.
To graph the equation, we can plot the y-intercept first, which is (0, 5). Then, using the slope, we can determine the next points on the graph.
From the y-intercept (0, 5), we can find the next point by moving 3 units to the right and 2 units up, as the slope is 2/3. This gives us the point (3, 7).
We can repeat this process to find more points on the graph. For example, moving 3 units to the right and 2 units up from the point (3, 7) gives us the point (6, 9).
By connecting these points on a graph, we get a straight line.
To identify the slope (m) and the y-intercept (b) of the equation y = (2/3)x + 5, we can use the standard form of a linear equation: y = mx + b.
In this equation, the coefficient of x is the slope, and the constant term is the y-intercept.
So, for the equation y = (2/3)x + 5:
Slope (m) = 2/3
Y-Intercept (b) = 5
Now let's graph the equation:
To graph the equation, we need to plot at least two points on the coordinate plane using the slope and y-intercept.
1. Start by plotting the y-intercept: (0, 5). This is the point where the line intersects the y-axis.
2. To find the second point, use the slope (2/3). The slope tells us that for every increase of 3 units on the x-axis, the y-value increases by 2 units.
Starting from the y-intercept (0, 5), move 3 units to the right and 2 units up. Plot this point.
You now have two points plotted: (0,5) and (3, 7).
3. Connect the two plotted points with a straight line.
The resulting line represents the graph of the equation y = (2/3)x + 5.
Here is a description of the steps you can use to graph the equation:
1. Plot the y-intercept at the point (0, b).
2. Use the slope (m = rise/run) to find a second point.
- The rise is the change in y-values (numerator of the slope).
- The run is the change in x-values (denominator of the slope).
- Starting from the y-intercept, move the run units to the right and the rise units up or down to find the second point.
3. Plot the second point.
4. Connect the two points with a straight line to graph the equation.