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2 years ago

a line with the slope of 1/3 passes through the points of (6,0). what is the equation in slope intercept form?

Mathematics

1 answer:

sleet_krkn [62]2 years ago

8 0

Answer:

y = 1/3x -2

Step-by-step explanation:

the equation for slope intercept form is y= mx + b.

m is the slope and b is where the line crosses the y-axis which is called the y-intercept.

to find the y-intercept plug in a coordinate on the line (6,0)

0 = 1/3(6) + b

then solve for b by first multiplying 1/3 by 6

0 = 2 + b

subtract 2 from both sides

-2 = b

and then you can plug b into the equation

y = 1/3x - 2

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<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\$

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$Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)$

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

$y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\$

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The figure that is not equivalent to 2¾ is 2¼ × 2½. That is option B.

<h3>Simplification of equivalent fractions</h3>

Simplification is a process that is used to make a fraction appear in its simplest forms.

The fraction given is = 2¾

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But simplification of 2¼ × 2½ is equal to;

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2½= 1

Therefore 2¾ is not equivalent to 2¼ × 2½ when simplified.

Learn more about fraction here:

brainly.com/question/78672

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1 year ago

a line with the slope of 1/3 passes through the points of (6,0). what is the equation in slope intercept form?​

a line with the slope of 1/3 passes through the points of (6,0). what is the equation in slope intercept form?