Question

find the equation of line passing through the points (-3,4) and (4,5)​

Answer 1

Recall:

Equation of a linear line can be placed in the format:

$y = mx + c$

Formula for finding the gradient of the line:

$m = \dfrac{Y_2 - Y_1}{X_2 - X_1}$

Given:

The two points are (-3, 4) and 4, 5)

Find the gradient:

$m = \dfrac{Y_2 - Y_1}{X_2 - X_1}$

$m = \dfrac{5 - 4}{4- (-3)}$

$m = \dfrac{1}{7}$

Form the intermediate equation:

$y = mx + c$

$y = \dfrac{1}{7} x + c$

Find the y-intercept:

Substitute (-3, 4) into the equation

$y = \dfrac{1}{7} x + c$

$4 = \dfrac{1}{7} (-3) + c$

$4 = -\dfrac{3}{7} + c$

$c = 4 + \dfrac{3}{7}$

$c = \dfrac{31}{7}$

Form the equation:

$y = \dfrac{1}{7} x + c$

$y = \dfrac{1}{7} x + \dfrac{31}{7}$

$7y = x + 31$

Answer: The equation of the line is 7y = x + 31