Respuesta :
Answer:
The equation of line is:
[tex]77x+4y=340[/tex]
Step-by-step explanation:
Given points:
[tex](0,85)[/tex] and [tex](4,8)[/tex]
To find the equation of the line.
Solution:
In order to find the equation of the line we will first find the slope of the line.
The slope of a line passing through points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] the slope can be given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging in the given points to find the slope of the line.
[tex]m=\frac{8-85}{4-0}[/tex]
[tex]m=\frac{-77}{4}[/tex]
Equation of line can be written in point slope form as:
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on the line.
Using point (4,8)
[tex]y-8=-\frac{77}{4}(x-4)[/tex]
Multiplying both sides by 4.
[tex]4(y-8)=4.(-\frac{77}{4})(x-4})[/tex]
[tex]4(y-8)=-77(x-4)[/tex]
Using distribution:
[tex]4y-32=-77x+308[/tex]
Subtracting [tex]4y[/tex] both sides.
[tex]4y-4y-32=-77x-4y+308[/tex]
[tex]-32=-77x-4y+308[/tex]
Subtracting 308 both sides.
[tex]-32-308=-77x-4y+308-308[/tex]
[tex]-340=-77x-4y[/tex]
Multiplying each term with -1.
[tex]340=77x+4y[/tex]
Thus, equation of line is:
[tex]77x+4y=340[/tex]
