Considering the definition of a line and the x- and y-intercept, the attached graph is obtained.
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.
In this case, if x=0, you replace this value in the equation y=-1/2x-3:
y= -1/2×0 -3
Solving:
y= 0 -3
y= -3
The y-intercept is (x;y)= (0; -3).
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.
In this case, if y=0, you replace this value in the equation y=-1/2x-3:
0= -1/2x -3
Solving:
3= -1/2x
3÷(-1/2)=x
-6= x
The x-intercept is (x;y)= (-6; 0).
Graphic
Considering the x- and y-intercepts, the attached graph is obtained.