Question

Y=4x-4, passing through the point (-8,-1) and perpendicular

Answer 1

The equation of the line perpendicular to
`\(y = 4x - 4\)` and passing through the point
`\((-8, -1)\) is \(y = -(1)/(4)x - 3\).`

Step-by-step explanation:

To find the equation of a line perpendicular to
`\(y = 4x - 4\)`, we recognize that the slopes of perpendicular lines are negative reciprocals. The given line has a slope of 4, so the perpendicular line has a slope of
`\(-(1)/(4)\).`

Using the point-slope form
`\(y - y_1 = m(x - x_1)\),` where
`\((x_1, y_1)\)` is the given point
`\((-8, -1)\)`, we substitute the values to obtain the equation
`\(y = -(1)/(4)x - 3\).` The negative sign indicates the perpendicular relationship, and
`\(-3\)` is the y-intercept.

This result ensures that the new line not only has the desired slope but also passes through the specified point. Understanding the relationship between slopes and perpendicular lines is fundamental to solving such problems in coordinate geometry.