If we are given a linear equation that has both x and y in it and need to find the slope, we put the equation into slope-intercept form. This is the equation that results from getting y by itself on one side of the equal sign. The formula for the slope intercept form of a line is

If the equation has only x in it, the slope will be undefined.(Since every point has the same x value, the denominator of the slope formula would be 0)

If the equation has only y in it the slope will be 0.(Since every point has the same y value, the numerator of the slope formula would be 0)

If the denominator of the fraction is 0, the slope is undefined. This occurs if the x value is the same for both points. The graph would be a vertical line and would indicate that the x value stays constant for every value of y.

If the numerator of the fraction is 0, the slope is 0. This will happen if the y value of both points is the same. The graph would be a horizontal line and would indicate that the y value stays constant for every value of x.

If the slope of a line is positive, it would slant this way: /
If the slope is positive, then an increase in x would mean an increase in y.

If the slope of a line is negative, it would slant this way: \
If the slope is negative, then an increase in x would mean a decrease in y.

Because all lines with the same slope will slant at the same angle, parallel lines have the same slope. Perpendicular lines (lines that intersect at a 90 degree angle) have slopes that are negative reciprocals.
If we are given two equations and asked if they are parallel or perpendicular, we first find the slope by putting the equation into slope-intercept form.