A.
The slope of a line is the rate of change of the dependent variable (y) with respect to the independent variable (x).
Notice that for each increase of 3 units in the variable x, the variable y decreases 2 units. Then, the change in y is -2 when the change in x is 3. Then, the rate of change is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{-2}{3}[/tex]
B.
The y-intercept of a line is the value of y in which the line crosses the Y-axis. In this case, the line crosses the Y-axis at y=4. Then, the y intercept is:
[tex]4[/tex]
C.
Similarly, the x-intercept is the value of x in which the line crosses the X-axis. In this case, we can see that the x-intercept is:
[tex]6[/tex]
D.
Since the slope m is equal to -2/3 and the y-intercept b is equal to 4, then the equation of the line is:
[tex]y=-\frac{2}{3}x+4[/tex]
