Considering the expression of a line, the points of the x-intercept and y-intercept are (4, 0) and (0,-3) respectively, and the graph is attached.
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 and represents the coordinate of the point where the line crosses the y axis.
Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.
Definition of y-intercept
The 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.
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.
Equation in this case
In this case, being the points of the x-intercept and y-intercept are (x₁, y₁)= (4, 0) and (x₂, y₂)= (0,-3) respectively, the slope m can be calculated as:
m= (-3 -0)÷ (0 - 4)
m= (-3)÷ (-4)
m= 3/4
Considering point 1 and the slope m, you obtain:
0= 3/4×4 + b
0= 3 +b
0 -3= b
-3= b
Finally, the equation of the line is y=3/4x -3.
In summary, the points of the x-intercept and y-intercept are (4, 0) and (0,-3) respectively, and the graph is attached.