Considering the definition of a line and the y-intercept, the graph is attached.
A linear equation o line can be expressed in the form y = mx + b
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin.
The ordinate to the origin or y-intercept is the point where a line crosses the y-axis. To find the y-intercept of a function, you simply do x = 0 and replace in the equation of the line. Then you solve the equation you obtained.
The x-intercept is the point where a line crosses the y-axis. To find the x-intercept of a function, you simply do y = 0 and replace in the equation of the line. Then you solve the equation you obtained.
If x=0, you replace this value in the equation 3x-2y=6:
3×0-2y=6
Solving:
0-2y=6
-2y=6
y= 6÷(-2)
y= -3
Finally, the y-intercept is (x;y)= (0; -3).
If y=0, you replace this value in the equation 3x-2y=6:
3x-2×0=6
Solving:
3x-0=6
3x=6
x= 6÷(3)
x= 2
Finally, the y-intercept is (x;y)= (2; 0).
Finally, the graph is attached.