Question

Find an equation in slope-intercept form for a line perpendicular to y = -2x - 1 and passing through (-10, 4).

A) y = 2x + 14
B) y = -2x + 4
C) y = 0.5x - 1
D) y = -0.5x + 4

Answer 1

y = -(1/2)x + 9

Step-by-step explanation:

We want to find the equation of a perpendicular line that passes through a reference line of y = -2x - 1.

Wen using the slope-intercept format of y = mx + b, m is the slope and b is the y-intercept (the value of y when x is zero), we know that any perpendicular line will have a slope that is the negative inverse of the reference line's slope, of -2 (m).

Since m = -2, the slope of a perpendicular line will be -(-1/2) or (1/2)

The new line takes the form y = (1/2)x + b.

To find b, use the given point (-10,4) and solve for b:

y = (1/2)x + b.

4 = (1/2)(-10) + b. for (-10,4)

4 = -5 + b

b = 9

The new line perpendicular to y = -2x - 1 and intersecting (-10,4) is:

y = -(1/2)x + 9

See the attached graph.

Answer 2

To find an equation in slope-intercept form for a line perpendicular to y = -2x - 1 and passing through (-10, 4), determine the slope of the given line, find its negative reciprocal, and use the point-slope form to plug in the coordinates of the given point and the determined slope.

Step-by-step explanation:

To find an equation in slope-intercept form for a line perpendicular to y = -2x - 1 and passing through (-10, 4), we need to determine the slope of the given line and find its negative reciprocal. The given line has a slope of -2, so the perpendicular line will have a slope of 1/2. Using the point-slope form of a linear equation, we can plug in the coordinates of the given point and the determined slope to find the equation of the perpendicular line.

Using the point-slope form: y - y1 = m(x - x1)

Plugging in the values: y - 4 = (1/2)(x + 10)

Converting to slope-intercept form: y = (1/2)x + 5 + 4

Simplifying: y = (1/2)x + 9

Therefore, the equation in slope-intercept form for the line perpendicular to y = -2x - 1 and passing through (-10, 4) is y = (1/2)x + 9.