Answer:
Explanation:
To graph the equation y-2=2/3(x+4), you can follow these steps:
Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:
y-2+2=2/3(x+4)+2
y=2/3(x+4)+2
Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):
y=2/3(x+4)+2
y=(2/3)x+(2/3)4+2
y=(2/3)x+8/3+2
y=(2/3)x+14/3
This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.
To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.
From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:
y2=y1+m(x2-x1)
y2=14/3+2/3(1-0)
y2=14/3+2/3
y2=20/3
You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept