Question

The line equation through point (1,-5) and perpendicular to line y = 2x +5 is​

Answer 1

The equation of the line through the point (1, -5) and perpendicular to the line y = 2x + 5 is 2y + x + 9 = 0

Discussion :

The general form of a straight line equation :

ax + by + c = 0

ax + by = c or

y = mx + c

with:

x and y = variable

a, b, c, and m = constants

↓↓↓↓↓↓

Known :

point (1, -5)

equation y = 2x + 5

m₁ = 2

Asked: Line equation?

Answer :

The vertical line gradient with the line gradient y = 2x + 5, namely :

m₁ x m₂ = -1

2 x m₂ = -1

m₂ = -1/2

Enter m into the equation of the line through points (1, -5) and gradient -1/2 :

y - y1 = m (x - x1)

y - (-5) = -1/2 (x - 1)

y + 5 = -1 / 2x + 1/2

y = -1 / 2x + 1/2 - 5

y = -1 / 2x + 1/2 - 10/2

y = -1 / 2x - 9/2

2y = -x - 9

2y + x + 9 = 0

Answer 2

Step-by-step explanation:

y = -4x + 17

Explanation:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.