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Archy [21]
2 years ago
9

Write an equation in slope-intercept form for the following line: (-14,1) and (13,-2)

Mathematics
1 answer:
alex41 [277]2 years ago
4 0

Answer:

\large \boxed{y =  -  \frac{1}{9} x -  \frac{5}{9} }

Step-by-step explanation:

In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.

\large \boxed{m =  \frac{y_2 - y_1}{x_2 - x_1} }

m-term is defined as slope in y = mx+b form which is slope-intercept form.

Now we substitute these ordered pairs (x, y) in the formula.

\large{m =  \frac{1 - ( - 2)}{ -14 - 13} } \\  \large{m =  \frac{1 + 2}{ - 27} } \\  \large{m =  \frac{3}{ - 27}  =  -  \frac{1}{9} }

After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is

\large \boxed{y = mx + b}

We already know m-value as we substitute it.

\large{y =  -  \frac{1}{9} x  + b}

We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)

We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.

\large{y = -  \frac{1}{9} x + b} \\  \large{ - 2 =  -  \frac{1}{9} (13) + b} \\  \large{ - 2 =  -  \frac{13}{9}  + b} \\  \large{ - 2 +  \frac{13}{9}  = b} \\  \large{ -  \frac{5}{9}  = b}

Finally, we know b-value. Then we substitute it in our equation.

\large{y =  -  \frac{1}{9} x + b} \\  \large{y =  -  \frac{1}{9} x -  \frac{5}{9} }

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Step-by-step explanation:

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

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Subtract sides 2x

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Divide sides by 3

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

CHECK :

2x + 9 = 5x

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So the value is correct.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

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