Question

what is the equation of this linear function? y = ?x +

Explanation:

Step1: Identify two points

The line passes through \((0, -2)\) (y - intercept) and \((1, -4)\).

Step2: Calculate the slope (\(m\))

Slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \((x_1,y_1)=(0, - 2)\) and \((x_2,y_2)=(1, - 4)\), we get \(m=\frac{-4 - (-2)}{1 - 0}=\frac{-2}{1}=-2\).

Step3: Determine the y - intercept (\(b\))

From the point \((0, -2)\), when \(x = 0\), \(y=-2\), so \(b = - 2\).

Step4: Write the equation

Using the slope - intercept form \(y=mx + b\), substitute \(m=-2\) and \(b = - 2\). So the equation is \(y=-2x-2\).

Answer:

The equation of the linear function is \(y = - 2x-2\) (the slope is \(-2\) and the y - intercept is \(-2\), so filling in the blanks: the first blank is \(-2\) and the second blank is \(-2\)).