Slopes and more

Given a line between two points, (x1,y1) and (x2,y2), find the slope. The formula is:

            y2 - y1
            -------
            x2 - x1
        

You can type in arithmetic expressions into the text boxes. However, you still need to indicate whether the slope is negative or not. If the slope is negative, change the answer to "Is slope NEGATIVE?" to Yes by tapping on the blue button next to the question.

The slope is undefined if the denominator, which is x2 - x1, equals 0. Change the answer to "Is slope UNDEFINED?" to Yes by tapping on the blue button next to the question. You can leave the numerator and denominator of the slope blank if the slope is undefined.

Find the unique solution (x,y), if any, where Line 1 and Line 2 intersect. It is recommended that you use the Substitution Method to solve the linear system:

1. Substitute the value of y from the Line 1 equation into the Line 2 equation. Solve for x.
2. Substitute the value for x that you found into the Line 1 equation. Solve for y.

If the slopes of the two lines are the same but the lines have different y-intercepts, then the two lines are inconsistent and there is no solution for the linear system. If the two lines are inconsistent, change the answer to "Inconsistent?" to Yes by tapping on the blue button next to the question.

If two lines have the same slope and the same y-intercept, then the two lines are dependent and there are an infinite number of solutions. Change the answer to "Dependent?" to Yes by tapping on the blue button next to the question if the two lines are dependent.

Are the two lines perpendicular, parallel, or neither?

If you multiply the slopes of the two lines together and get -1, then the lines are perpendicular. (The slopes of perpendicular lines are negative reciprocals.) Change the answer to "Perpendicular?" to Yes by tapping on the blue button next to the question if the two lines are perpendicular.

If the slopes of the two lines are the same, then the lines are parallel. Change the answer to "Parallel?" to Yes by tapping on the blue button next to the question if the two lines are parallel.

If the lines are neither perpendicular nor parallel, then leave the answers to the two questions as No.

Find the slope-intercept form for the line with the given slope which passes through the given point. The slope-intercept form of a linear equation has the general form:

        y = mx + b
        

where m is the slope and b is the y-intercept.

Here are the recommended steps:

1. Convert the slope from decimal to SIMPLIFIED fractional form. For example, 0.8 is 8 / 10 which can be simplified to 4 / 5. Enter the numerator (e.g. 4) and denominator (e.g. 5) in the first two text boxes. Use the left button for the sign.
2. Substitute x and y from the given point and solve for the y-intercept (b) in the general form above. Enter the absolute value (make it positive if it is negative) into the last text box. Tap the button to the left of the text box to change the sign to - if the y-intercept value is negative.