Answer:
- Equation of Parallel line: y = -5x-34
- Equation of Perpendicular line: y = 1/5x - 14/5
Step-by-step explanation:
a) Equation of Parallel line to the given line and passes through the point (-6, -4)
We know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given the line
y = -5x+4
comparing with the slope-intercept form of the line equation
The slope of the line = m = -5
We know that parallel lines have the same slope. Thus, the slope of the line parallel to the line y = -5x+4 will also be: -5
So, the equation of the line parallel to the given line and passes through the point (-6, -4) will be:
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -5 and the point (-6, -4)
y - (-4) = -5(x-(-6))
y+4 = -5(x+6)
y+4 = -5x-30
y = -5x-30-4
y = -5x-34
Therefore, the the equation of the line parallel to the given line and passes through the point (-6, -4) will be:
Hence:
Equation of Parallel line: y = -5x-34
a) Equation of Parallel line to the given line and passes through the point (-6, -4)
Given the line
y = -5x+4
comparing with the slope-intercept form of the line equation
The slope of the line = m = -5
We know that a line to perpendicular another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
The slope of new line = – 1/m = -1/-5 = 1/5
So, the equation of the line perpendicular to the given line and passes through the point (-6, -4) will be:
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 1/5 and the point (-6, -4)
y - (-4) = 1/5 (x-(-6))
y+4 = 1/5 (x+6)
Subtract 4 from both sides
[tex]y+4-4=\frac{1}{5}\left(x+6\right)-4[/tex]
[tex]y=\frac{1}{5}x-\frac{14}{5}[/tex]
Therefore, the equation of the line perpendicular to the given line and passes through the point (-6, -4) will be:
[tex]y=\frac{1}{5}x-\frac{14}{5}[/tex]
Hence:
Equation of Perpendicular line: y = 1/5x - 14/5
