Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Answer:

$y = - \frac{1}{6} x + 2$

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

Let's first identify the coordinates of two points on the graph:

(-6, 3) and (6, 1)

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

Slope

$= \frac{3 - 1}{ - 6 - 6}$

$= \frac{2}{ - 12}$

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

Substitute the value of the slope into m in the equation:

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

To find the value of c, substitute a pair of coordinates into the equation.

When x= 6, y= 1,

$1 = - \frac{1}{ 6} (6) + c$

1= -1 +c

c= 1 +1

c= 2

Thus, the equation of the line is y= -⅙x +2.

The y-intercept can also be derived from the graph as we can see that the line passes through the y- axis at (0, 2). This point can also be used to find the slope of the line too.

Answer 2

Answer:

you can write the equation of any line in the form of y = mx + b .

Step-by-step explanation: