Question

Write the equation of the line, given the y and x-intercepts.
y-intercept = 23, x-intercept = 4.75

Answer 1

Answer:

The equation of the line in slope intercept form is  $y=-\frac{92}{19}x+23$

The equation of the line in standard form is $92x+19y=437$

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

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0-23}{4.75-0}$

$m=-\frac{23}{4.75}$

$4.75=4\frac{3}{4}=\frac{19}{4}$

substitute

$m=-\frac{23}{(19/4)}$

$m=-\frac{92}{19}$

Determine the equation of the line in slope intercept form

$y=mx+b$

we have

$m=-\frac{92}{19}$

$b=23$ ----> the y-intercept

substitute

$y=-\frac{92}{19}x+23$

see the attached figure to better understand the problem

write the equation of the line in standard form

$Ax+By=C$

where A is a positive integer

B and C are integers

$y=-\frac{92}{19}x+23$

Multiply by 19 both sides to remove the fraction

$19y=-92x+437$

Adds 92x both sides

$92x+19y=437$