4.7.4 Writing Equations From Two Points

Algebra 14.7.4 Writing Equations From Two Points

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With a partner, use what you have learned to write an equation in each form from two points.

Find the slope of the line that goes through $(2, 3)$ and $(6, - 4)$ .

Compare your answer: $- \frac{7}{4}$

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 4 - 3}{6 - 2} = - \frac{7}{4}$

Write the equation of the line in point-slope form that goes through $(2, 3)$ and $(6, - 4)$ .

Compare your answer:

Answer: $y - 3 = - \frac{7}{4} (x - 2)$ or $y + 4 = - \frac{7}{4} (x - 6)$

Using the point $(2, 3)$ :

$y - y_{1} = m (x - x_{1})$

$y - 3 = - \frac{7}{4} (x - 2)$

Using the point $(6, - 4)$ :

$y - y_{1} = m (x - x_{1})$

$y - (- 4) = - \frac{7}{4} (x - 6)$

$y + 4 = - \frac{7}{4} (x - 6)$

Write the equation of the line in slope-intercept form that goes through $(2, 3)$ and $(6, - 4)$ . (Hint: use the equation from number 2)

Compare your answer:

Answer: $y = - \frac{7}{4} x + \frac{13}{2}$

$y - 3 = - \frac{7}{4} (x - 2)$

$y - 3 = - \frac{7}{4} x + \frac{14}{4}$

$y - 3 = - \frac{7}{4} x + \frac{7}{2}$

$y - 3 + 3 = - \frac{7}{4} x + \frac{7}{2} + 3$

$y = - \frac{7}{4} x + \frac{7}{2} + \frac{6}{2}$

$y = - \frac{7}{4} x + \frac{13}{2}$

Write the equation of the line in standard form that goes through $(2, 3)$ and $(6, - 4)$ .

(Hint: use the equation from number 3.)

Compare your answer:

Answer: $7 x + 4 y = 26$

$4 (y = - \frac{7}{4} x + \frac{13}{2})$

$4 y = - 7 x + 26$

$4 y + 7 x = - 7 x + 7 x + 26$

$7 x + 4 y = 26$

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