Mathematics, 11.12.2020 02:10 sassycutie523

Write an equation of line that passes through the points (4,3) land (1, 2) in point-slope form.

Answers: 3

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Answer from: anaroles04

$y=\frac{1}{3} x+\frac{5}{3}$

Step-by-step explanation:

Use the slope formula to find the slope:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}$

Insert the values:

$(4_{x_{1}},3_{y_{1}})\\\\(1_{x_{2}},2_{y_{2}})\\\\\frac{2-3}{1-4}=\frac{-1}{-3}=\frac{1}{3}$

The slope is 1/3.

You can do this two ways. You can solve using slope-intercept and solve for b, or use point-slope form, then simplify to slope-intercept

Use the slope-intercept form:

y=mx+b

where:

m is the slopeb is the y-interceptx and y are corresponding coordinate points (x,y)

Insert the slope and one of the given coordinate points:

$(1_{x},2_{y})\\\\2=\frac{1}{3} (1)+b$

Solve for the y-intercept. Simplify:

$2=\frac{1}{3} +b$

Subtract 1/3 from both sides:

$2-\frac{1}{3} =\frac{1}{3} -\frac{1}{3} +b\\\\2-\frac{1}{3} =b$

Subtract. Find the common denominator:

$\frac{6}{3} -\frac{1}{3} =\frac{5}{3}$

Insert:

$\frac{5}{3} =b$

The y-intercept is 5/3. Insert:

$y=\frac{1}{3}x+\frac{5}{3}$

Use point-slope form:

$y-y_{1}=m(x-x_{1})$

where:

m is the slopex1 and y1 are corresponding coordinate points

Insert values:

$(1_{x_{1}},2_{y_{1}})\\\\y-2=\frac{1}{3} (x-1)$

Simplify the equation by solving for y. This will result in the slope-intercept form. Simplify multiplication using the rule $\frac{a}{b} *c=\frac{ac}{b}$ :

$y-2=\frac{1(x-1)}{3} \\\\y-2=\frac{x-1}{3}$

Isolate the variable. Add 2 to both sides:

$y-2+2=\frac{x-1}{3} +2\\\\y=\frac{x-1}{3}+2$

Simplify to slope-intercept form, y=mx+b. Use the rule $\frac{a-b}{c} =\frac{a}{c}-\frac{b}{c}$ :

$y=\frac{x}{3} -\frac{1}{3} +2$

Combine like terms. Find a common denominator:

$-\frac{1}{3}+2=-\frac{1}{3}+\frac{2}{1}\\\\-\frac{1}{3}+\frac{3*2}{3*1}=-\frac{1}{3}+\frac{6}{3} \\\\-\frac{1}{3}+\frac{6}{3} =\frac{5}{3}$

Insert:

$y=\frac{x}{3} +\frac{5}{3}$

Use the rule $\frac{x}{a} =\frac{1}{a}x$ :

$y=\frac{1}{3} x+\frac{5}{3}$

:Done

Answer from: Quest

what's that

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

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←

add

94.09

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Write an equation of line that passes through the points (4,3) land (1, 2) in point-slope form....

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