Find the equation of a line l in each case and write it instandard form with integral coefficients. a) line l has y-intercept (0,5) and x- intercept (4,0) b) line l has slope 5 and goes through (0,1/2)

Graham Beasley

Graham Beasley

Answered question

2022-07-27

Find the equation of a line l in each case and write it instandard form with integral coefficients.
a) line l has y-intercept (0,5) and x- intercept (4,0)
b) line l has slope 5 and goes through (0,1/2)

Answer & Explanation

Reese King

Reese King

Beginner2022-07-28Added 13 answers

a) The equation for a line is y = mx + b
where m is the slope and b is the y intercept.
Therefore, the slope is rise over run, which is -5/4 and the yintercept is 5
y = -5x/4 + 5
b) slope is 5 and y intercept is 1/2
y = 5x + 1/2
Ruby Briggs

Ruby Briggs

Beginner2022-07-29Added 3 answers

(A) Line 1 has a y-intercept (0, 5) and x-intercept (4,0)
So, x 1 = 0 , y 1 = 5 , x 2 = 4 , y 2 = 0
Use the definition of slope formula:
m = y 2 y 1 x 2 x 1
m = 0 5 4 0
m = 5 4
Use the point-slope formula:
m = 5 4 , x 1 = 0 , y 1 = 5
y y 1 = m ( x x 1 )
y 5 = 5 4 ( x 0 )
y = 5 4 x + 5 Equation of the line inslope-intercept form y=mx+b
5 4 x + y = 5
Multiply through the equation by 4.
5x+4=20 Equation of the line instandard form: Ax+By=C
(B) Line 1 has a slope of 5 and goes through (0, 1/2)
x 1 = 0 , y 1 = 1 2 , m = 5
Use the point-slope formula:
y y 1 = m ( x x 1 )
y 1 2 = 5 ( x 0 )
y = 5 x + 1 2 Equation of the line given inslope-intercept form y=mx+b
5 x + y = 1 2
5 x y = 1 2 Equation of the line given instandard form: Ax+By=C

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