How do you write the equation in slope intercept form given (1,1):(3,2)?

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How do you write the equation in slope intercept form given (1,1):(3,2)?

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Answer 1 · 2017-06-09T22:51:11

$y = \frac{1}{2} x + \frac{1}{2}$ $y=1/2x+1/2$

Explanation:

Algebraic form is $A x + B y = C$ $Ax+By=C$ where $A, B$ $A, B$ and $C$ $C$ are constants that depend on the question.
Slope-intercept form is $y = m x + c$ $y=mx+c$ where $m$ $m$ is the gradient and $(0, c)$ $(0,c)$ is the $y$ $y$ -intercept.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$ for a line containing the points $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ .

For $(1, 1)$ $(1,1)$ and $(3, 2)$ $(3,2)$ ,
$m = \frac{2 - 1}{3 - 1}$ $m=(2-1)/(3-1)$
$m = \frac{1}{2}$ $m=1/2$

Therefore, $y = \frac{1}{2} x + c$ $y=1/2x+c$ . To find c, substitute $(1, 1)$ $(1,1)$ into this equation.
$1 = \frac{1}{2} \times 1 + c$ $1=1/2×1+c$
$c + \frac{1}{2} = 1$ $c+1/2=1$
$c = \frac{1}{2}$ $c=1/2$

Substitute $c$ $c$ value back into equation,
$y = \frac{1}{2} x + \frac{1}{2}$ $y=1/2x+1/2$

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How do you write the equation in slope intercept form given (1,1):(3,2)?

1 Answer

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