Considering the definition of a line and the x and y-intercept, the y-intercept of the line that represented by the equation: x -4y= 18 is (0;-9/2). and the x-intercept is (18;0). The graph is attached.
Definition of linear equation
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.
Definition of y-intercept
The ordinate to the origin 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.
Definition of x-intercept
The x.intercept is the point where a line crosses the x-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.
y-intercept in this case
If x=0, you replace this value in the equation x - 4y = 18:
0 - 4y = 18
Solving:
-4y= 18
y= 18÷ (-4)
y= -9/2
Finally, the y-intercept is (x;y)= (0; -9/2).
x-intercept in this case
If y=0, you replace this value in the equation x - 4y = 18:
x - 4×0 = 18
Solving:
x - 0= 18
x= 18
Finally, the x-intercept is (x;y)= (18; 0).