Question

Write the equation of the line, given the y and x-intercepts.

y-intercept = 23, x-intercept = 4.75

Answer 1

The equation of the line in slope intercept form is
`y=-(92)/(19)x+23`

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

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=(y2-y1)/(x2-x1)`

substitute the values

`m=(0-23)/(4.75-0)`

`m=-(23)/(4.75)`

`4.75=4(3)/(4)=(19)/(4)`

substitute

`m=-(23)/((19/4))`

`m=-(92)/(19)`

Determine the equation of the line in slope intercept form

`y=mx+b`

we have

`m=-(92)/(19)`

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

substitute

`y=-(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=-(92)/(19)x+23`

Multiply by 19 both sides to remove the fraction

`19y=-92x+437`

Adds 92x both sides

`92x+19y=437`