Question

Write an equation for the line parallel to the line
shown that passes through the point (-2.3)

Answer 1

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

To find the slope, we need two points, according to the graph we have:

`(x_ {1}, y_ {1}) :( 0,3)\\(x_ {2}, y_ {2}) :( 1,0)`

The slope is:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-3} {1-0} = \frac {-3} {1} = -3`

Therefore, the equation is of the form:

`y = -3x + b`

By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:

`y = -3x + b`

We substitute the point through which the line passes and find "b":

`3 = -3 (-2) + b\\3 = 6 + b\\3-6 = b\\b = -3`

Finally, the equation is:

`y = -3x-3`

ANswer:

`y = -3x-3`