Line Equation Lab
Slide the slope and the intercept to build any line on the coordinate grid. Watch all three equation forms update live, then take on six build-a-line challenges.
1 Build a line
Drag the sliders. The dashed right triangle shows the slope: run 2 along the grid, rise up (or down) the line. The red dot is the y-intercept — the line’s starting point.
2 Build-a-line challenges
Read each challenge, set the sliders above to match the described line, then press Check. Solving all six means you can translate any description of a line into an equation.
3 What do you notice?
Play with the sliders and confirm each of these — they are the whole story of y = mx + b.
Changing m pivots the line around the red dot — the pivot point is (0, b). Changing b slides the line straight up or down without tilting it. Those two moves are independent: b sets where, m sets how steep.
Positive m climbs left to right; negative m falls. Set m = 0 and the line goes perfectly flat: y = b — every point has y-coordinate b. (There is no vertical line here: a vertical line has no slope and no y = mx + b form.)
Set b = 0, then compare m = 1/2, 1, 2, 4: the line gets steeper as |m| grows. The triangle makes it concrete — for m = 3, every run of 2 climbs a rise of 6.
Slide around, then read the three forms side by side. Point-slope remembers the data you started with; slope-intercept is ready to graph; standard is the tidy integer form. Same line, three costumes.