Read coordinates in the stated horizontal/vertical order.
Connect points to values that satisfy an equation.
Calculate and interpret a slope with its units.
Read the axes before the line
Check which quantity belongs on each axis, its units, and the size of each interval. A point (x, y) describes the horizontal coordinate first and the vertical coordinate second.
Connect a rule to the plotted values
A point on the graph of an equation satisfies that equation. For a straight line, slope is vertical change divided by horizontal change; its meaning depends on the quantities and units.
A mistake to avoid
A graph can look steeper after changing the axis scales without changing the underlying rate. Calculate the numerical changes instead of comparing the drawn angle alone.
Worked example
Read y = 2x + 1
When x = 0, y = 1; when x = 2, y = 5. The points (0, 1) and (2, 5) lie on the line. Its slope is (5 − 1)/(2 − 0) = 2, and its vertical intercept is 1.
Learning paths that include this skill
Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.