Final answer:
The lines represented by the equations Y=x and x+y= -2 are perpendicular to each other because their slopes are negative reciprocals of each other (1 and -1, respectively). Slopes come in 4 different types: negative, positive, zero, and undefined. as x increases.
Step-by-step explanation:
To determine whether the lines represented by the equations Y=x and x+y= -2 are parallel, perpendicular, or neither, we first need to rearrange each equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
The first equation is already in slope-intercept form with slope = 1.
To convert the second equation, we can rewrite it as y = -x - 2, which reveals a slope = -1.
Since the slopes of the two lines are negative reciprocals of each other (1 and -1), the lines are perpendicular to one Slope tells us how steep a line is. It's like measuring how quickly a hill goes up or down. We find the slope by seeing how much we go up or down (vertical change) for each step to the right (horizontal change). If a line goes up 2 steps for every 1 step to the right, its slope is 2.
The slope, or steepness, of a line is found by dividing the vertical change (rise) by the horizontal change (run). The formula is slope =(y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line.