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3 years ago

Choose the equation that represents a line that passes through points (-1, 2) and (3, 1).

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

8 0

Answer:

Step-by-step explanation:

$\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\==============================$

$\text{We have the points (-1, 2) and (3, 1). Substitute:}\\\\m=\dfrac{1-2}{3-(-1)}=\dfrac{-1}{4}=-\dfrac{1}{4}\\\\\text{Put the value of a slope and the coordinates of the point (3, 1) }\\\text{to the equation of a line:}\\\\y-1=-\dfrac{1}{4}(x-3)\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y-1=-\dfrac{1}{4}(x-3)\qquad\text{multiply both sides by 4}\\\\4y-4=-(x-3)\\\\4y-4=-x-(-3)\qquad\text{add x to both sides}\\\\x+4y-4=3\qquad\text{add 4 to both sides}\\\\x+4y=7$

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The system of equation used to find the Total number of flash cards made are $\left \{ {{5x+5} \atop {6x}} \right.$ .

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Step-by-step explanation:

Given:

Number of flash cards already made by Tristan = 5

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Let the number of minutes be $'x'$ .

Now we can say that;

Total number of flash cards made by Tristan is equal to Number of flash cards already made by Tristan plus Number of flash card Tristan makes in 1 min multiplied by number of minutes.

framing in equation form we get;

Total number of flash cards made by Tristan = $5+5x$

Also We can say that;

Total number of flash cards made by Josh is equal Number of flash card Josh makes in 1 min multiplied by number of minutes.

framing in equation form we get;

Total number of flash cards made by Josh = $6x$

Hence the system of equation used to find the Total number of flash cards made are $\left \{ {{5x+5} \atop {6x}} \right.$ .

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$5+5x=6x$

On solving we get;

Combining like terms we get;

$6x-5x=5\\\\x=5\ mins$

Hence It would take 5 minutes when both will have same number of flash cards.

To find the number of flash cards each would had at that time we will substitute value of $x=5$ in the system of equations.

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number of flash cards made by Tristan = $5x+5 = 5\times5+5=25+5=30$

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