Question #76df0

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Question #76df0

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Answer 1 · 2016-12-18T03:47:52

The equation would be $y = m x + b$ $y = mx + b$

Explanation:

B is the y intercept, the point of the line that touches some part of the y-axis.

M is the slope (rise over run). You find it by plugging two points on the line into the slope equation: $m = \frac{y_{2} - y_{1}}{X_{2} - x_{1}}$ $m = (y_2 - y_1)/(X_2 - x_1)$ .

Y is basically the linear function.

So if I have a line with the equation: $y = 2 x + 1$ $y = 2x + 1$

I can plug in values for $x$ $x$ and $y$ $y$ (let's say 1). I replace $x$ $x$ with 1 so --> $y = 2 (1) + 1$ $y = 2(1) + 1$ . SO if $x$ $x$ is 1, then I can solve the equation and say $y = 3$ $y = 3$ . That's one point (1, 3) on the line of the equation above. Another value to find another point. $b$ $b$ is 1 because $y$ $y$ = 2 $x$ $x$ + 1. That means at (x, $1$ $1$ ) the line touches the y-axis.

And as I gave the equations above, when you find the second coordinate (the first being (1, 3)) by plugging in another value for $x$ $x$ and solving for $y$ $y$ , you can find $m$ $m$ , the slope.

Answer 2 · 2016-12-18T04:09:06

Perhaps the question refers to the "intercept form" of a line:

$\frac{x}{a} + \frac{y}{b} = 1$ $x/a +y/b=1$ ,
where the $x$ $x$ intercept is $(a, 0)$ $(a,0)$ and the $y$ $y$ intercept is $(0, b)$ $(0,b)$ .

To convert this form to slope intercept form $y = m x + b$ $y=mx+b$ (where $m$ $m$ is the slope and $b$ $b$ is the $y$ $y$ intercept),

multiply the equation $\frac{x}{a} + \frac{y}{b} = 1$ $x/a +y/b=1$ by the LCD $a b$ $ab$

$a b (\frac{x}{a} + \frac{y}{b} = 1)$ $ab(x/a +y/b =1)$

$\frac{a b x}{a} + \frac{a b y}{b} = a b$ $(abx)/a +(aby)/b=ab$

$b x + a y = a b$ $bx+ay=ab$
$- b x a a a - b x$ $-bxcolor(white)(aaa)-bx$

$a y = - b x + a b$ $ay=-bx+ab$

$\frac{a y}{a} = \frac{- b x}{a} + \frac{a b}{a}$ $(ay)/a=(-bx)/a+(ab)/a$

$y = (- \frac{b}{a}) x + b$ $y=(-b/a)x +b$

So, to convert from the "intercept form" of a line $\frac{x}{a} + \frac{y}{b} = 1$ $x/a+y/b=1$
to the "slope intercept form" $y = m x + b$ $y=mx+b$ ,

the slope $m = - \frac{b}{a}$ $m=-b/a$ and the y intercept $b$ $b$ is equal to the "b" in the intercept form.

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Question #76df0

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