Question

Complete the point-slope equation of the line through (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis and (7,4)(7,4)left parenthesis, 7, comma, 4, right parenthesis. Use exact numbers. y-4=y−4=y, minus, 4, equals

Answer 1

Answer:

$y = \frac{1}{5}x +\frac{13}{5}$

Step-by-step explanation:

Given

$(x_1,y_1) = (2,3)$

$(x_2,y_2) = (7,4)$

Required

Complete the equation y - 4.....

First, we need to determine the slope as follows:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4 - 3}{7 - 2}$

$m = \frac{1}{5}$

The equation is then calculated as thus:

$y - y_1 = m(x - x_1)$

This gives:

$y - 4 = \frac{1}{5}(x -7)$

Open bracket

$y - 4 = \frac{1}{5}x -\frac{7}{5}$

Add 4 to both sides

$y - 4 +4= \frac{1}{5}x -\frac{7}{5} + 4$

$y = \frac{1}{5}x -\frac{7}{5} + 4$

$y = \frac{1}{5}x +\frac{-7+20}{5}$

$y = \frac{1}{5}x +\frac{13}{5}$