Question

Write an equation that represents the line (use exact numbers)

Answer 1

Answer:

$y = x + 6$

Step-by-step explanation:

Given

The attached graph

Required

Find the equation of the graph

First, we have to get the coordinates of any two points on the graph;

Point 1:

When x = 0; y = 6

Point 2:

When x = -6, y = 0

So, at this stage;we have two coordinates

$(x_1,y_1)(x_2,y_2) = (0,6)(-6,0)$

Next is to determine the slope of the line using the following formula

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

Substitute $(x_1,y_1)(x_2,y_2) = (0,6)(-6,0)$

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

$m = \frac{0 - 6}{-6 - 0}$

$m = \frac{- 6}{-6}$

$m = 1$

Next is to determine the equation using slope formula

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

using

$m = \frac{y - y_1}{x - x_1}\ where\ m = 1\ x_1 = 0\ and \ y_1 = 6$

$1 = \frac{y - 6}{x - 0}$

$1 = \frac{y-6}{x}$

Multiply both sides by x

$x * 1 = x * \frac{y-6}{x}$

$x = y - 6$

Add 6 to both sides

$x + 6 = y - 6 + 6$

$x + 6 = y$

$y = x + 6$

Hence, the equation of the line is $y = x + 6$