Get the answer to "Find the equation of the straight lines that..."

siroticuvj

Answered question

2021-11-14

Find the equation of the straight lines that pass through the following sets of points:
a)

(2; 4); (4; 7)

(3; - 5); (- 2; 2)

(1; 3); (- 3; 1)

Answer & Explanation

barcelodurazo0q

Beginner2021-11-15Added 13 answers

Step 1
Equation of line that passes through the points $(x_{1}, y_{1}) (x_{2}, y_{2})$ is:
$y - y_{1} = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})} ((x - x_{1})$
where,
slope $m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$
Step 2
a) Given points $(2, 4) (4, 7)$
now
$x_{1} = 2$
$y_{1} = 4$
$x_{2} = 4$
$y_{2} = 7$
Equation of a line:
$y - 4 = \frac{(7 - 4)}{(4 - 2)} ((x - 2)$
$y - 4 = \frac{3}{2} (x - 2)$
$y = \frac{3}{2} x - \frac{6}{2} + 4$
$y = \frac{3}{2} x + 1$
Step 3
Given points $(3, - 5) (- 2, 2)$
now
$x_{1} = 3$
$y_{1} = - 5$
$x_{2} = - 2$
$y_{2} = 2$
Equation of a line:
$y + 5 = \frac{(2 + 5)}{(- 2 - 3)} (x - 3)$
$y + 5 = - \frac{7}{5} (x - 3)$
$y = - \frac{7}{5} x + \frac{21}{5} - 5$
$y = - \frac{7}{5} x - \frac{4}{5}$
Step 4
Given points $(1, 3) (- 3, 1)$
now
$x_{1} = 1$
$y_{1} = 3$
$x_{2} = - 3$
$y_{2} = 1$
Equation of a line:
$y - 3 = \frac{(1 - 3)}{(- 3 - 1)} (x - 1)$
$y - 3 = \frac{1}{2} (x - 1)$

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