Help please! Explain step by step how. THANKS!?

Question

1. Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6).

2. Write the equation of a line in point-slope form that has a slope of and passes through the point (2, -7).

3.Write the equation of a line in slope intercept form that is parallel to the line and passes through (-9, 5).

Answer 1

1). Given that the perpendicular line equation is y = - 4x

Here slope(m) is -4 but it's perpendicular(-1/m), so the slope(m) will be 1/4.

And  point is (2, 6)

Recall: The 'slope-point' equation form is (y - y₁) = m(x - x₁)

y - 6 = (1/4)(x - 2)

Multiply each side by 4.

4(y - 6) = x - 2

4y - 24 = x - 2

Add 24 to each side.

4y = x + 22

Divide each side by 4.

y = (1/4)(x + 22).

Comments

Thank you!! could please answer to other questions too. :)

Answer 2

• (1).

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

Line equation is y = - 4x and the point is (2, 6).

Compare the above line equation with slope - intercept form of line equation is y = mx + b.

Slope (m) = - 4.

 

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line is 1/4.

Now, the perpendecular line equation is y = (1/4)x + b.

 

Find the y - intercept by substituting the point in the perpendecular line equation say (x, y) = (2, 6).

6 = (1/4)(2) + b

b = 6 - 1/2

b = (12 - 1)/2

⇒ b = 11/2.

The perpendecular line equation  is y = (1/4)x + (11/2).

Answer 3

• (2).

Point - slope form of a line equation is y - y₁ = m(x - x₁), where m is slope of the line, and (x₁, y₁) is the point lies on the line.

The line equation is y = - 4x.

Compare the above line equation with slope - intercept form of line equation is y = mx + b.

Slope = - 4.

Let, Slope (m) = - 4 and the point (x₁, y₁) = (2, - 7).

Point - slope form of the line is

y - (- 7) = (- 4)(x - 2)

y + 7 = (- 4)(x - 2).

Point - slope form of the line equation is y + 7 = (- 4)(x - 2).

• (3).

The line equation is y = - 4x.

Compare the above line equation with slope - intercept form of line equation is y = mx + b.

Slope = - 4.

Because the parallel lines have same slopes, the slope of parallel line through the point (- 9, 5) is - 4.

Now the parallel line equation is y = - 4x + b.

Find the y - intercept by substituting the point in the parallel line equation say (x, y) = (- 9, 5).

5  = (- 4)(- 9) + b

b = 5 - 36

⇒ b = - 31.

The parallel line equation is y = - 4x - 31.