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2 years ago

Determine if the lines are parallel perpendicular or neither x-3y=15 and y=-3x+4

Mathematics

1 answer:

geniusboy [140]2 years ago

8 0

Answer: Perpendicular

Step-by-step explanation:

Convert both equations into slope-intercept form

$y=-3x+4$ ⇒ $y=-3x+4$

$x-3y=15$ ⇒ $y=\frac{1}{3} x-5$

Determine the slope of each equation

$y=-3x+4$ : SLOPE = -3

$y=\frac{1}{3} x-5$ : SLOPE = 1/3

When two lines are parallel to each other, their slopes will be the same. However, since -3 does not equal 1/3, they are not parallel

$-3\neq \frac{1}{3}$

When two lines are perpendicular to each other, the product of their slopes will be -1. Since -3 multiply by 1/3 is -1, they are perpendicular to each other.

$(-3)*(\frac{1}{3} )=-1$

Hope this helps!! :)

Please let me know if you have any questions

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quotient 9.2 x 10^6/ 2.3 x 10²
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Another method would be to expand both numbers then divide and do scientific notation again.
Remember to change to normal notation you move the decimal to the right using the number of the exponent.

9.2 x 10^6= 9200000
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Use the method that is best for you or just know you can use either method to check your work.

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

alex41 [277]

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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