This skill appears in almost every Algebra 1 course on DeltaMath, usually in the Linear Functions unit right before slope from two points and slope-intercept form. The problem shows one line on a grid and the instruction is short: find the slope.
Slope is a ratio. It compares how far the line rises (or falls) to how far it runs to the right between any two points on the line. Because the ratio is the same everywhere on a straight line, you can choose whichever two points are easiest to read.
How to solve it, step by step
Find two lattice points on the line
A lattice point is where the line passes exactly through a grid intersection. If DeltaMath marks two dots, use those. If not, follow the line with your eye until it crosses a corner cleanly. Points on the axes (the intercepts) are often the easiest.
Count the rise between them
Start at the left point. Count how many grid squares you move up (positive) or down (negative) to reach the height of the right point. Write the number with its sign.
Count the run
Now count how many squares you move to the right to land on the second point. Because you always move left to right, the run is positive.
Write slope = rise ÷ run and reduce
For example, rise 4 and run 6 gives 4/6, which reduces to 2/3. If the rise divides evenly by the run, give an integer (6/3 = 2). If the rise is negative, the fraction is negative (−3/2).
Sanity-check the sign
A line that goes up from left to right has positive slope; one that goes down has negative slope. A flat line has slope 0; a vertical line has undefined slope.
Worked example
A line passes through (−4, −3) and (2, 1). Find its slope.
- Left point: (−4, −3) Right point: (2, 1)
- Rise: from y = −3 up to y = 1 → 1 − (−3) = 4
- Run: from x = −4 right to x = 2 → 2 − (−4) = 6
- Slope = rise / run = 4 / 6 = 2 / 3
Answer m = 2/3
A line crosses the y-axis at (0, 5) and passes through (3, −1).
- Rise: from 5 down to −1 → −1 − 5 = −6
- Run: from 0 to 3 → 3
- Slope = −6 / 3 = −2
Answer m = −2 (the line falls 2 for every 1 to the right)
Mistakes DeltaMath marks wrong
- Counting run over rise (x over y). Slope is always the vertical change on top.
- Dropping the negative sign when the line falls from left to right.
- Using a point that only looks like it sits on a grid corner. Zoom in or pick the intercepts instead.
- Forgetting to reduce: DeltaMath accepts 4/6 on most problems, but a reduced fraction avoids formatting surprises.
- Reading a vertical line as slope 0. Vertical lines have undefined slope; horizontal lines have slope 0.
How to type the answer
- Type fractions with a slash: 2/3, -3/2.
- Type integers without a slash: 2, -1, 0.
- For a vertical line choose or type "undefined" if the problem allows it.