This formula can be restated as the rise over the run. It is the change in vertical difference over the change in horizontal difference, or the steepness of the line. If a line points upwards to the right, it will have a positive slope. If the line is downwards to the right, it will have a negative slope.

Points are easily determined when you have a line drawn on graphing paper. To define a point, draw a dashed line up from the horizontal axis until it intersects the line. The position that you started the line on the horizontal axis is the X coordinate, while the Y coordinate is where the dashed line intersects the line on the vertical axis. For example: line l has the points (1, 5) and (-2, 4) while line r has the points (3, 3) and (1, -4).

To calculate the slope of line l: slope = (5 – (-4))/(1 – (-2)) Subtract: slope = 9/3 Divide: slope = 3 The slope of line r is: slope = (3 – (-4))/(3 - 1) = 7/2

In this example, 3 is not equal to 7/2, therefore, these two lines are not parallel.

For example. Rewrite 4y - 12x = 20 and y = 3x -1. The equation 4y - 12x = 20 needs to be rewritten with algebra while y = 3x -1 is already in slope-intercept form and does not need to be rearranged.

For example: Rewrite line 4y-12x=20 into slope-intercept form. Add 12x to both sides of the equation: 4y – 12x + 12x = 20 + 12x Divide each side by 4 to get y on its own: 4y/4 = 12x/4 +20/4 Slope-intercept form: y = 3x + 5.

In our example, the first line has an equation of y = 3x + 5, therefore it’s slope is 3. The other line has an equation of y = 3x – 1 which also has a slope of 3. Since the slopes are identical, these two lines are parallel. Note that if these equations had the same y-intercept, they would be the same line instead of parallel. [11] X Research source

The following steps will work through this example: Write the equation of a line parallel to the line y = -4x + 3 that goes through point (1, -2).

The line we want to draw parallel to is y = -4x + 3. In this equation, -4 represents the variable m and therefore, is the slope of the line.

In our example, we will use the coordinate (1, -2).

Using our example with slope (m) -4 and (x, y) coordinate (1, -2): y – (-2) = -4(x – 1)

For example: y – (-2) = -4(x – 1) Two negatives make a positive: y + 2 = -4(x -1) Distribute the -4 to x and -1: y + 2 = -4x + 4. Subtract -2 from both side: y + 2 – 2 = -4x + 4 – 2 Simplified equation: y = -4x + 2