Question

Please help me with this​

Answer 1

• Equation of Parallel line: y = -5x-34

• Equation of Perpendicular line: y = 1/5x - 14/5

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

`y = mx+b`

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

`y-y_1=m\left(x-x_1\right)`

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:

• y = -5x-34

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

`y-y_1=m\left(x-x_1\right)`

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

`y+4-4=(1)/(5)\left(x+6\right)-4`

`y=(1)/(5)x-(14)/(5)`

Therefore, the equation of the line perpendicular to the given line and passes through the point (-6, -4) will be:

`y=(1)/(5)x-(14)/(5)`

Hence:

Equation of Perpendicular line: y = 1/5x - 14/5