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dimaraw [331]
3 years ago
15

Can someone show me how to write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)?

Mathematics
1 answer:
8090 [49]3 years ago
3 0

Answer:

\large\boxed{y=\dfrac{2}{3}x+\dfrac{1}{3}\qquad\text{slope-intercept form}}\\\\\boxed{y-1=\dfrac{2}{3}x-\dfrac{2}{3}\qquad\text{point-slope form}}\\\\\boxed{2x-3y=-1\qquad\text{standard form}}

Step-by-step explanation:

\text{The standard form:}\ Ax+By=C

\text{The point-slope form:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\\text{We have the slope}\ m=\dfrac{2}{3}\ \text{and the point}\ (1,\ 1).\ \text{Substitute:}\\\\\underline{y-1=\dfrac{2}{3}(x-1)}\qquad\text{use the distributive property}\\\\y-1=\dfrac{2}{3}x-\dfrac{2}{3}\qquad\text{add 1 to both sides}\\\\\underline{y=\dfrac{2}{3}x+\dfrac{1}{3}}

y=\dfrac{2}{3}x+\dfrac{1}{3}\qquad\text{multiply both sides by 3}\\\\3y=2x+1\qquad\text{subtract 2x from both sides}\\\\-2x+3y=1\qquad\text{change the signs}\\\\\underline{2x-3y=-1}

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Chance has hired a construction crew to renovate his kitchen. They charge $3.55 per square foot for materials and $121.26 per da
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Step-by-step explanation:

Chance has hired a construction crew to renovate his kitchen

  • They charge $3.55 per square foot for materials
  • They charge $121.26 per day of labor
  • Chance spent $2,450.24 on the renovation
  • The number of square feet is 198 more than the number of days it took for the renovation

We need to find for how long the renovation took

Assume that the renovation took x days

∵ The renovation took x days

∵ The number of square feet is 198 more than the number of days

∴ The number of square feet = x + 198

∵ They charge $3.55 per square foot

∵ They charge $121.26 per day of labor

∴ The cost of renovation = 3.55(x + 198) + 121.26(x)

- Simplify the expression

∴ The cost of renovation = 3.55 x + 702.9 + 121.26 x

- Add like terms

∴ The cost of renovation = 124.81 x + 702.9

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- Equate the cost of renovation by the money that Chance spent

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∴ 124.81 x + 702.9 = 2,450.24

- Subtract 702.9 from both sides

∴ 124.81 x = 1,747.34

- Divide both sides by 124.81

∴ x = 14

The renovation took 14 days

Learn more:

You can learn more about word problems in brainly.com/question/10557938

#LearnwithBrainly

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