Answer:
The equation of the line in slope intercept form is [tex]y=-\frac{92}{19}x+23[/tex]
The equation of the line in standard form is [tex]92x+19y=437[/tex]
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
The y-intercept is the point (0,23)
The x-intercept is the value of x when the value of y is equal to zero
so
The x-intercept is the point (4.75,0)
therefore
we have the points
(0,23) and (4.75,0)
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0-23}{4.75-0}[/tex]
[tex]m=-\frac{23}{4.75}[/tex]
[tex]4.75=4\frac{3}{4}=\frac{19}{4}[/tex]
substitute
[tex]m=-\frac{23}{(19/4)}[/tex]
[tex]m=-\frac{92}{19}[/tex]
Determine the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{92}{19}[/tex]
[tex]b=23[/tex] ----> the y-intercept
substitute
[tex]y=-\frac{92}{19}x+23[/tex]
see the attached figure to better understand the problem
write the equation of the line in standard form
[tex]Ax+By=C[/tex]
where A is a positive integer
B and C are integers
[tex]y=-\frac{92}{19}x+23[/tex]
Multiply by 19 both sides to remove the fraction
[tex]19y=-92x+437[/tex]
Adds 92x both sides
[tex]92x+19y=437[/tex]
