The equation of a line in the form y = mx + c has the slope equal to m. Two parallel lines have an equal slope and the product of the slope of perpendicular lines is equal to -1.
For y = -2x + 3, the slope is -2 and for y = -x + 4, the slope is -1. As the two lines do not have the same slope they are not parallel. Also -2*-1 `!=` -1. This shows that the lines are not perpendicular.
The equation 3y + 7 = 4x should be represented in the form y = mx + c to find the slope.
3y + 7 = 4x
=> 3y = 4x - 7
=> y = (4/3)x - 7/3
The slope of the line is `4/3` .
The lines y = -2x + 3 and y = -x + 4 are neither parallel nor perpendicular. The slope of 3y + 7 = 4x is `4/ 3`