Considering the definition of parallel line, the equation of line l is y= -5x -11.
<h3>Linear equation</h3>
A linear equation o line can be expressed in the form y = mx + b
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
<h3>Parallel line</h3>
Parallel lines are two lines that are always at the same distance from each other.
Two lines are parallel if they have the same slope and different y-intercepts. This is, they have the same value of m and different value of b.
<h3>Equation of parallel line in this case</h3>
In this case, the line is y−3=−5(x−2) Expressed in the form y = mx + b, you get:
y−3=−5x−2×(-5)
y−3=−5x+ 10
y=−5x+ 10 + 3
<u><em>y= -5x +13</em></u>
where:
- the slope is -5.
- the y-intercept is 13.
Two lines are parallel if they have the same slope. So, the parallel line has a slope of -5 and has a form of: y= -5x + b
The line passes through the point (3, -26). Replacing in the expression for parallel line:
-26= -5× 3 + b
-26= -15 + b
-26 + 15 = b
<u><em>-11 = b</em></u>
Finally, the equation of parallel line is y= -5x -11.
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