Final answer:
The equation of a vertical line passing through (-3,4) is x = -3, and the equation of a horizontal line through this point is y = 4. These are special cases in line equations where the usual slope-intercept form y = mx + b is not used.
Step-by-step explanation:
To write the equation of a vertical line passing through the given point (-3,4), recall that a vertical line has an undefined slope and all points on that line have the same x-coordinate. Therefore, the equation will simply be x = -3.
To write the equation of a horizontal line passing through the given point (-3,4), remember that a horizontal line has a slope of zero and all points on that line will have the same y-coordinate. The equation of this line is y = 4.
The b and m terms in an equation of a straight line, as in y = mx + b, determine the shape of the line where 'm' represents the slope and 'b' represents the y-intercept. However, for vertical and horizontal lines, which are special cases, we use the equations as described above.