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)

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)

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

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

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:

$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$

$m=\frac{0-5}{4-0}$

$m=-\frac{5}{4}$

Use the point-slope formula:

$m=-\frac{5}{4},{x}_{1}=0,{y}_{1}=5$

$y-{y}_{1}=m(x-{x}_{1})$

$y-5=-\frac{5}{4}(x-0)$

$y=-\frac{5}{4}x+5$ 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:

$y-{y}_{1}=m(x-{x}_{1})$

$y-\frac{1}{2}=5(x-0)$

$y=5x+\frac{1}{2}$ 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

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:

$m=-\frac{5}{4},{x}_{1}=0,{y}_{1}=5$

$y-{y}_{1}=m(x-{x}_{1})$

$y-5=-\frac{5}{4}(x-0)$

$y=-\frac{5}{4}x+5$ 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:

$y-{y}_{1}=m(x-{x}_{1})$

$y-\frac{1}{2}=5(x-0)$

$y=5x+\frac{1}{2}$ 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

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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