Question

Write an equation of the line passes through (-4,4) y=1/2x+1

Answer 1

Answer: y = -2x - 4

The equation of the line given is

`(1)/(2)x\text{ + 1}`

The slope - intercept form of equation is written as

y = mx + b

Where m = slope and b = intercept

From the above equation

m = 1/2

For a perpendicular line

`\begin{gathered} For\text{ perpendicular line} \\ m1\text{ x m2 = -1} \\ m1\text{ = }(1)/(2) \\ \text{Therefore,} \\ (1)/(2)\text{ x m2 = -1} \\ \text{Make m2 the subject of the formula} \\ m2\text{ = }(-1)/((1)/(2)) \\ m2\text{ = -1 x }(2)/(1) \\ m2\text{ = -2} \end{gathered}`

Since m2 = -2

Hence, the perpendicular equation can be calculated

(y - y1) = m(x - x1)

The given point is ( -4, 4)

x1 = -4 and y1 = 4, and m = -2

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

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

Open the parenthesis

y - 4 = -2x - 2*4

y - 4 = -2x - 8

y = -2x -8 + 4

y = -2x - 4