Graham Beasley

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

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

(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:
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$
$m=\frac{0-5}{4-0}$
$m=-\frac{5}{4}$
Use the point-slope formula:
$m=-\frac{5}{4},{x}_{1}=0,{y}_{1}=5$
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
$y-5=-\frac{5}{4}\left(x-0\right)$
$y=-\frac{5}{4}x+5$ Equation of the line inslope-intercept form y=mx+b
$\frac{5}{4}x+y=5$
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)
${x}_{1}=0,{y}_{1}=\frac{1}{2},m=5$
Use the point-slope formula:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
$y-\frac{1}{2}=5\left(x-0\right)$
$y=5x+\frac{1}{2}$ Equation of the line given inslope-intercept form y=mx+b
$-5x+y=\frac{1}{2}$
$5x-y=-\frac{1}{2}$ Equation of the line given instandard form: Ax+By=C

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