Question

ip. writing equations in slope-intercept form - day 2

1. which equation can be written into slope-intercept form

a ( y = -3x^2 + 4 )

b ( xy = -2 )

c ( y = -2x )

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

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Linear equations are of degree 1 (the highest power of \(x\) is 1).

Step2: Analyze Option A

The equation \(y=- 3x^{2}+4\) is a quadratic equation (the highest power of \(x\) is 2). Quadratic equations have the form \(y = ax^{2}+bx + c\) (\(a
eq0\)) and cannot be written in the linear slope - intercept form \(y=mx + b\) since it has a squared term.

Step3: Analyze Option B

The equation \(xy=-2\) can be rewritten as \(y=\frac{-2}{x}=-2x^{-1}\). This is a rational function (inverse variation) and not a linear function. The power of \(x\) is \(- 1\), not 1, so it cannot be written in slope - intercept form.

Step4: Analyze Option C

The equation \(y = - 2x\) is already in the slope - intercept form \(y=mx + b\) where \(m=-2\) and \(b = 0\).

(Assuming Option D has a typo or is not a linear form, but from the given options, Option C is linear and in slope - intercept form or can be considered as such with \(b = 0\))

Answer:

C. \(y=-2x\)