Question

what is the equation of the line in slope-intercept form that passes through the point (-2,4) and is perpendicular to the line y=-2x+4?

Answer 1

do you know the relationship between the gradients of two perpendicular lines?

Answer 2

nope

Answer 3

they are negative reciprocals of each other so if the gradient of line 1 is m the gradient for the one perpendicular to it is -1/m, so in the line you have in the question, can you see the gradient?

Answer 4

y=mx+b is the formula right?

Answer 5

right

Answer 6

whats gradient?

Answer 7

gradient is the slope, given by m in your equation and b is the y-intercept, so in y = -2x +4 , what's the gradient?

Answer 8

-2?

Answer 9

so what is the gradient of the line perpendicular to this one?

Answer 10

2

Answer 11

remember, if one is m, the other is -1/m, i.e the negative reciprocal,try again

Answer 12

let me assist you, since m is -2 , then -1/m becomes (-1)/(-2) this is equal to a half (1/2), got it?

Answer 13

yes

Answer 14

good, now to answer the question we have the coordinates (-2,4) and (x,y) and the gradient 1/2, remember, gradient also defined as the (change in y )/ (change in x), can you proceed from here?

Answer 15

:(

Answer 16

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

Answer 17

2y-8 = x+2
2y =x+10
y = 1/2x +5
this is the equation of your line,
look at its gradient

Answer 18

alright thanks!