Question 1

Write an equation in point-slope form of the line that passes through the point (5,6) with slope 3/5

Question 2

Answer:

$\boxed{y - 6 = (3)/(5) (x - 5)}$

Explanation:

Given:

Formula:

$y - y_(1) = m(x - x_(1) ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{m = Slope}; \ (x_1},y_(1)) = \text{Coordinates of point}]$

Substitute the values into point slope form to determine the equation of the line in point slope form.

$\implies y - y_(1) = m(x - x_(1) )$

$\implies \boxed{y - 6 = (3)/(5) (x - 5)}$

Question 3

point-slope form:

slope intercept form:

Equation:

$\sf \hookrightarrow y-6 = (3)/(5) (x-5)$
$\sf [ \ this \ is \ point \ slope \ form \ equation \ ]$

$\sf \hookrightarrow y-6 = (3)/(5) x-3$ ----------------

$\sf \hookrightarrow y= (3)/(5) x-3+6$ -------------------

$\sf \hookrightarrow y= (3)/(5) x+3$
$\sf [ \ this \ is \ slope \ intercept \ form \ equation \ ]$

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