How do I find the equation of a linear function that passes through $(1, 7)$ $(1, 7)$ and $(2, 9)$ $(2, 9)$ ?

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How do I find the equation of a linear function that passes through $(1, 7)$ $(1, 7)$ and $(2, 9)$ $(2, 9)$ ?

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Answer 1 · 2014-09-17T23:20:41

For this type of problem we have 3 distinct steps to follow.

1) Find the slope using the formula $m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$ $m=((y_2-y_1))/((x_2-x_1))$

2) Find the y-intercept, $b$ $b$ , by substituting in the slope , $m$ $m$ , from STEP 1 and the $x$ $x$ and $y$ $y$ values from one of the points given in the slope intercept formula, $y = m x + b$ $y=mx+b$

3) Substitute the slope, $m$ $m$ , and the y-intercept, $b$ $b$ , back into the slope intercept formula, $y = m x + b$ $y=mx+b$ .

STEP 1

$x_{1} = 1$ $x_1=1$
$y_{1} = 7$ $y_1=7$

$x_{2} = 2$ $x_2=2$
$y_{2} = 9$ $y_2=9$

$m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})} = \frac{(9 - 7)}{(2 - 1)} = \frac{2}{1} = 2$ $m=((y_2-y_1))/((x_2-x_1))=((9-7))/((2-1))=2/1=2$

STEP 2

$y = m x + b$ $y=mx+b$

I will use the $x$ $x$ and $y$ $y$ values from the point $(1, 7)$ $(1,7)$

$7 = (2) (1) + b$ $7=(2)(1)+b$
$7 = 2 + b$ $7=2+b$
$5 = b$ $5=b$

STEP 3

$y = m x + b$ $y=mx+b$

$y = 2 x + 5 \leftarrow S O L U T I O N$ $y=2x+5 larr SOLUTION$

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How do I find the equation of a linear function that passes through $(1, 7)$ $(1, 7)$ and $(2, 9)$ $(2, 9)$ ?

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