Question

Which equation represents this line in point-slope form?

(y+4)=4/3(x+3)

(y−4)=−4/3(x+3)

y=−3/4x

4y−3x=0

Answer 1

(y-4) = -4/3(x+3) since formula for point slope is (y - y1) = m(x - x1)

Answer 2

Formular for equation is
y = mx + b

The gradient of the line
= y1 - y2/x1 - x2
= 4 - (-4)/(-3) - 3
= 8/-6
= -1⅓

Sub in the values to the formular:
4 = -1⅓(-3) + b
4 = 4 + b
b = 0

∴ Equation for this graph is y = -1⅓x

For each of the options, simplify and match the equation.

Option 1:
(y + 4) = 1⅓(x + 3)
y + 4 = 1⅓x + 4
y = 1⅓x (wrong)

Option 2:
(y - 4) = -1⅓(x + 3)
y - 4 = -1⅓x - 4
y = -1⅓x (answer matches)

∴ Answer is B.