# How do I determine if the lines y=-2x+3 and y=-x+4 are parallel, neither, or perpendicular. What is the slope of 3y+7=4x?

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### 1 Answer

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`