Question

Find the equation of the line
perpendicular to the line y=4x-4and passing through (-2,6)

Answer 1

✦ Given that

• A certain line is perpendicular to y = 4x - 4 and passes through (-2,6)

✦ We need to find

• The equation of the line

`\hrulefill`

If lines are perpendicular, their gradients are negative inverses.

`\longleftrightarrow\textrm{Negative inverse of 4 = -1/4}`

Equation:

`\longleftrightarrow\rm{y-y_1=m(x-x_1)}`

`\longleftrightarrow\rm{y-6=-1/4(x-(-2)}`

`\longleftrightarrow\rm{y-6=-1/4(x+2)}`

`\longleftrightarrow\rm{y-6=-1/4x-0.5}`

`\longleftrightarrow\rm{y=-1/4x-0.5+6}`

`\longleftrightarrow\rm{y=-1/4x+5.5}`

`\therefore\;\;\;\;\;\longleftrightarrow\rm{y=-\cfrac{1}{4}x+5.5}`

`\hrulefill`

Answer 2

y = 1/4x - 5.5

Explanation:

To find the equation of the line perpendicular to the line y = 4x - 4 and passing through (-2,6), we need to first determine the slope of the line y = 4x - 4.

m = 4

The slope of a line in slope-intercept form (y = mx + b) is equal to the coefficient of x (m). Therefore, the slope of the line y = 4x - 4 is 4.

Since we want to find the equation of a line that is perpendicular to this line, we know that the slope of our new line will be the negative reciprocal of 4. The negative reciprocal of 4 is -1/4.

Now we can use the point-slope form of a line to find the equation of the line perpendicular to y = 4x - 4 and passing through (-2,6). The point-slope form of a line is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Substituting our values into the equation, we get:

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

Simplifying, we get:

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

Multiplying both sides by -4 to eliminate the fraction, we get:

-4y + 24 = x + 2

Finally, we can rearrange this equation into standard form (Ax + By = C) by subtracting x from both sides:

-x + 4y = -22

4y = x - 22

y = 1/4x - 5.5