Slope on a One to One Grid
On a one-to-one grid, we can count slope using the boxes. Slope
The equation to calculate the coordinate from the coordinate on a line can be written in the form:
…where is the slope (also known as gradient or rate of change), and is the point on the line where the line cuts the axis, that is, the intercept.
When given two points, we can calculate slope using the formula
Once we know the slope, we can calculate the value by substituting one point in for the and ; or we can use the formula
The intercepts are points on the axes. To calculate the intercept, we substitute to the equation of the line. To calculate the intercept, we substitute to the equation of the line.
Vertical lines have an equation such as .
Horizontal lines have an equation such as .
Parallel lines have the same slope. E.g. and are parallel.
Perpendicular lines are lines that intersect at 90°. If the first line has slope then the second line will have slope : the negative reciprocal. Eg, the lines and are perpendicular. As another example, the lines and are perpendicular.
Use this applet to practice calculating the slope between two points; finding the equation of a line; calculating the y-intercept and calculating the x-intercept.