Slope on a One to One Grid
On a one-to-one grid, we can count slope using the boxes. Slope
Review
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.
Practice
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.