How do you write the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1)?

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How do you write the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1)?

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Answer 1 · 2016-05-27T19:19:19

$s l o p e = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $slope=(y_2-y_1)/(x_2-x_1)$
$y = - \frac{1}{5} x + \frac{7}{5}$ $y=-1/5x+7/5$

Explanation:

The slope of the line passing through the two points $(- 3, 2)$ $(-3,2)$ and $(2, 1)$ $(2,1)$ is given by

$s l o p e = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $slope=(y_2-y_1)/(x_2-x_1)$

$s l o p e = \frac{1 - 2}{2 - (- 3)}$ $slope=(1-2)/(2-(-3))$

$s l o p e = - \frac{1}{5}$ $slope =-1/5$

The equation of the straight line is

$y = a \cdot x + b$ $y=a*x+b$

$s l o p e = a = - \frac{1}{5}$ $slope = a=-1/5$

$y = - \frac{1}{5} x + b$ $y=-1/5x+b$

The point $(2, 1)$ $(2,1)$ is a point on the straight line. Plugging the coordinates of this point and the line equation allows us to find the Y-intercept.

$1 = - \frac{1}{5} \times 2 + b$ $1=-1/5xx2+b$

$b = 1 + \frac{2}{5}$ $b=1+2/5$

$b = \frac{7}{5}$ $b=7/5$

The equation of the straight-line will be

$y = - \frac{1}{5} x + \frac{7}{5}$ $y=-1/5x+7/5$

To find the X-intercept assign the value 0 to $y$ $y$

$0 = - \frac{1}{5} x + \frac{7}{5}$ $0=-1/5x+7/5$

$\frac{1}{5} x = \frac{7}{5}$ $1/5x=7/5$

$x = 7$ $x=7$

graph{-1/5*x+7/5 [-9.63, 10.37, -3.4, 6.6]}

Answer 2 · 2016-05-27T19:28:54

$y = \frac{- 1 x}{5} + \frac{7}{5}$ $y = (-1x)/5 + 7/5$

Explanation:

There are several ways of answering this question:

Method 1 . Use the two points to find the gradient $m$ $m$ .

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2 - y_1)/(x_2 - x_1)" "$ Then use one of the points as $(x, y)$ $(x,y)$

Substitute $m, x and y$ $m,x and y$ into $y = m x + c$ $y = mx + c$ and solve to find $c$ $c$ .

Now use the values for $m and c$ $m and c$ in $y = m x + c$ $y = mx + c$ to find the required equation.
This method is fine, but it requires several substitutions and it is easy to lose track of where you are.

Method 2 . Use the two points as $x and y$ $x and y$ and substitute each into $y = m x + c$ $y = mx + c " "$ This forms two equations which can be solved simultaneously to find m and c.

Method 3 . Use the two points as $(x_{1}, y_{1}) and (x_{2}, y_{2})$ $(x_1,y_1) and (x_2, y_2)$ and substitute into the formula for finding the equation of a line if 2 points are known: $\frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $" "(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)$

$\frac{y - 1}{x - 2} = \frac{2 - 1}{- 3 - 2}$ $" "(y - 1)/(x - 2) = (2 - 1)/(-3 - 2)$

$\frac{y - 1}{x - 2} = \frac{1}{- 5} now cross-multiply$ $" "(y - 1)/(x - 2) = 1/-5 " now cross-multiply"$

$- 5 (y - 1) = (x - 2) solve for y$ $-5(y - 1) = (x - 2) " solve for y"$

$- 5 y + 5 = x - 2$ $-5y + 5 = x - 2$

$- 5 y = x - 2 - 5$ $-5y " "= x -2 -5$

$y = \frac{- 1 x}{5} + \frac{7}{5} divide by -5$ $y = (-1x)/5 + 7/5 " divide by -5"$

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How do you write the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1)?

2 Answers

Explanation:

Explanation:

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