Final answer:
The linear equation that represents a line passing through the point (3, -4) with a slope of 2 is y = 2x - 10.
Step-by-step explanation:
To find the linear equation that represents a line passing through the point (3, -4) with a slope of 2, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
Using the given point (3, -4) and slope 2, we can substitute these values into the equation:
y - (-4) = 2(x - 3)
Simplifying,
y + 4 = 2x - 6
Finally, rearranging the equation to the slope-intercept form, y = mx + b,
y = 2x - 10