What is the equation of a line passing through (0,4) with slope -2?

The correct option is y = -2x + 4.

To find the equation of a straight line when given a point through which it passes and its slope, we can use the slope-intercept form of a linear equation:

$y=mx+c$

where:
• $m$ represents the slope of the line.
• $c$ represents the y-intercept (the value of $y$ when $x=0$).

Step 1: Identify the given values
• Slope, $m=-2$
• Point through which the line passes = $(0,4)$

Since the given point is $(0,4)$, the line crosses the y-axis at $y=4$. Therefore, the y-intercept $c$ is directly equal to $4$.

Step 2: Substitute the values into the slope-intercept form
Substituting $m=-2$ and $c=4$ into the equation $y=mx+c$:

$y=-2x+4$

Thus, the equation of the line is y = -2x + 4.