How do you write an equation in slope-intercept form of the line that passes through the points (-2, 6.9) and (-4, 4.6)?

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How do you write an equation in slope-intercept form of the line that passes through the points (-2, 6.9) and (-4, 4.6)?

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Answer 1 · 2018-04-13T05:32:59

$y = 1.15 x + 9.2 is the slope - intercept form$ $color(blue)(y = 1.15 x + 9.2 " is the slope - intercept form"$

$S l o p e = m = 1.15, y-intercept = 9.2$ $color(green)(Slope = m = 1.15, "y-intercept " = 9.2$

Explanation:

Equation of a line, knowing two points on it is given by

$\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$ $(y-y_1)/(y_2-y_1) = (x-x_1) / (x_2-x_1)$

$(x_{1}, y_{1}) = - 2, 6.9), (x_{2}, y_{2}) = (- 4, 4.6)$ $(x_1,y_1) = -2, 6.9), (x_2,y_2) = (-4, 4.6)$

$\frac{y - 6.9}{4.6 - 6.9} = \frac{x + 2}{- 4 + 2}$ $(y - 6.9) / (4.6 - 6.9) = (x +2) / (-4+2)$

$\frac{y - 6.9}{- 2.3} = \frac{x + 2}{- 2}$ $(y - 6.9) / -2.3 = (x + 2) / -2$

$(y - 6.9) = \frac{2.3 \cdot (x + 2)}{2}, cross multiplying$ $(y - 6.9) = (2.3 * (x + 2))/2, " cross multiplying"$

$y = 1.15 \cdot (x + 2) + 6.9$ $y = 1.15 * (x + 2) + 6.9$

$y = 1.15 x + 9.2 is the slope - intercept form$ $color(blue)(y = 1.15 x + 9.2 " is the slope - intercept form"$

$S l o p e = m = 1.15, y-intercept = 9.2$ $color(green)(Slope = m = 1.15, "y-intercept " = 9.2$

Answer 2 · 2018-04-13T05:34:55

$y = 1.15 x + 9.2$ $y=1.15x+9.2$

Explanation:

Since this is a linear variation of the form $y = m x + b$ $y=mx+b$ , any change in $x$ $x$ will create a proportional change in $y$ $y$ .
$(- 2) - (- 4) = 2$ $(-2)-(-4) = 2$ and
$(6.9) - (4.6) = 2.3$ $(6.9)-(4.6) = 2.3$ so
for every 2 changes in $x$ $x$ , $y$ $y$ changes by 2.3.
Divide each side by 2, and 1 change in $x$ $x$ corresponds to 1.15 in $y$ $y$ , therefore the slope ( $m$ $m$ ) must be 1.15.
Now we have the equation $y = 1.15 x + b$ $y=1.15x+b$
Before, we said our change in $x$ $x$ by 2 resulted in a change in $y$ $y$ of 2.3. Therefore, if we move over right 2 from $(- 2, 6.9)$ $(-2, 6.9)$ , we reach the point $(0, 9.2)$ $(0, 9.2)$ . Since the $x$ $x$ -value is 0, this is the y-intercept ( $b$ $b$ )
The equation is $y = 1.15 x + 9.2$ $y=1.15x+9.2$

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How do you write an equation in slope-intercept form of the line that passes through the points (-2, 6.9) and (-4, 4.6)?

2 Answers

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