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lorasvet [3.4K]
2 years ago
7

Write the equation for the line in slope-intercept form.

Mathematics
1 answer:
Elan Coil [88]2 years ago
6 0

Answer:

y = 4x + 3

Step-by-step explanation:

We are given the line shown in your question.

We want to write the equation of this line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept

As we are given the graph of the line, we can pick any 2 points to help us find the equation; in this case, let's take (0,3) and (-1, -1).

First, we need to find the slope of the line

The slope (m) can be found using the equation \frac{y_2-y_1}{x_2-x_1}, where (x_1, y_1) and (x_2, y_2) are points

Let's label the values of the points to avoid confusion and mistakes before calculating.

x_1= 0\\y_1=3\\x_2=-1\\y_2=-1

Now substitute these values into the equation for the slope

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

m=\frac{-1-3}{-1-0}

Subtract

m=\frac{-4}{-1}

Divide

m = 4

The slope of the line is 4

Here is the equation of the line so far:

y = 4x + b

Now we need to find b

As stated above, b is the value of y at the y intercept; the y intercept is the point where the line intersects with the y axis. The value of x at this point is 0

One of the points we used to calculate the slope was actually the y intercept point; this point is (0, 3). The value of y at this point is 3, so the value of b is 3

Substitute 3 as b in our equation

y = 4x + 3

Topic: finding the equation of the line

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Step-by-step explanation:

The point slope form of a straight line is expressed as

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=\frac{27}{125}

Step-by-step explanation:

0.216

\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}

\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000

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216,\:1000

\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}

2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}

=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3

2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}

=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5

\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}

=2\cdot \:2\cdot \:2

\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8

=8

=\frac{8\cdot \:27}{8\cdot \:125}

\mathrm{Cancel\:the\:common\:factor:}\:8

=\frac{27}{125}

Hence, the correct answer is =\frac{27}{125}

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