Question

an equation of the line that passes through the point (0, -1) and whose slope is 2 is
\\( y = 2x - 1 \\)
\\( y = -x + 2 \\)
\\( y = -2x - 1 \\)
\\( y = 2x + 2 \\)

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step2: Substitute given slope

We know the slope $m=2$, so the equation becomes $y = 2x + b$.

Step3: Substitute the given point

The line passes through $(0,-1)$, so substitute $x=0$, $y=-1$:
$-1 = 2(0) + b$

Step4: Solve for $b$

Calculate to find $b=-1$.

Step5: Write final equation

Substitute $b=-1$ back into $y = 2x + b$, getting $y = 2x - 1$.

Answer:

$y = 2x - 1$