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Genrish500 [490]
3 years ago
7

The given line passes through the points (0, ) and (2, 3). On a coordinate plane, a line goes through (0, negative 3) and (2, 3)

. A point is at (negative 1, negative 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point ()?

Mathematics
hyper manni
2 years ago
how you get the image in the question
2 answers:
yanalaym [24]3 years ago
7 1

Answer:

3rd and second

Step-by-step explanation:

Kipish [7]3 years ago
5 0

Answer:

y=\frac{x}{5}+\frac{12}{5}

Step-by-step explanation:

1) The Point-slope form equation is given in this form:

(x-x_{0})=m(y-y_{0})

2)Looking at the given graph, we can pick two points: (-5,-4) and (0,-3)

3) Before using the Point-slope form We have to find out the slope:

m=\frac{-4-(-3)}{0-(-5)} \Rightarrow m=\frac{-4+3}{0+5} \Rightarrow m=\frac{-1}{5}

4)Parallel lines share the same slope. The one that passes through (-2,2) is found by calculating its linear parameter "b":

y=\frac{x}{5}+b\Rightarrow 2=\frac{-2}{5}+b\\5*10=(-2+b)*5\Rightarrow 5b=12 \Rightarrow \frac{5b}{5} =\frac{12}{5} \Rightarrow b=\frac{12}{5}

Then, the answer is:

y=\frac{x}{5}+\frac{12}{5}

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Which inequality is represented by the graph? y≥35x−1.5 y≤35x−1.5 y&lt;35x−1.5 y&gt;35x−1.5
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Answer:

y > 0.6x - 1.5

Step-by-step Explanation:

We need two points, to get to the equation of the graph.

Since we've got the following equation for two points (x1, y1), (x2, y2):-

\boxed{ \mathsf{ \red{y - y_{1} =  \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})  }}}

okay soo

I found two points that lie on this graph, not on the shaded region but yeah the dotted line which defines the graph.

one point is <u>(0, -1.5)</u> which lies on the y axis(the point where the dotted line touches the y axis)

other point is <u>(2.5, 0)</u> and this lies on the x axis

placing these points in the place of (x1, y1) and (x2, y2) in the above mentioned equation

\mathsf{\implies y - ( - 1.5) =  \frac{0 -( - 1.5)}{2.5 -0 } (x -0 )}

you can take any one as (x1, y1) or (x2, y2).

so upon solving the above equation we get

\mathsf{\implies (y  +  1.5) =  \frac{0  +  1.5}{2.5  } (x  )}

\mathsf{\implies y  +  1.5 =  \frac{ 1.5}{2.5  } x  }

\mathsf{\implies y  +  1.5 =  \frac{ \cancel{1.5}\:\:{}^3}{\cancel{2.5}\:\:{}^5 } x  }

\mathsf{\implies y  +  1.5 =  \frac{ 3}{5 } x  }

multiplying both sides by 5

\mathsf{5y + 7.5 = 3x}

okay so this is the required equation of the dotted line

now we'll find the inequality

for this check whether the origin (0,0) lies under the shaded region or not

in this case it does

so

replacing x and y with 0

\mathsf{\implies5(0) + 7.5 = 3(0)}

\mathsf{\implies0 + 7.5 = 0}

this is absurd, 7.5 is not equal to 0 so we're gonna replace that equals sign with that of inequality

7.5 is greater than 0! so,

\mathsf{\implies7.5 > 0}

this goes for the whole equation, since we didnt swap any thing from left to right side of the equation or vice versa we can use this sign, to obtain the required inequality

\mathsf{5y + 7.5 > 3x}

dividing this inequality by 5, since there's no co-efficient in front of y in the given answers

we get

y + 1.5 > 0.6x

taking 1.5 to the RHS

<h3>y > 0.6x - 1.5 </h3>

that is the last option

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3 years ago
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