Question

Graph the linear equation y=2x−3

Answer 1

The equation is already in slope-intercept form y = mx + b with slope m = 2 and y‑intercept b = −3.

Steps to graph:
1. Plot the y‑intercept: (0, −3).
2. Use the slope 2 = rise/run = 2/1: from (0, −3) go up 2 and right 1 to get (1, −1). Repeat to get (2, 1), (3, 3)...
3. (Optional) Go left using the negative direction: from (0, −3) go down 2 and left 1 to get (−1, −5).
4. Draw a straight line through these points and extend it across the grid.

Key points:
- y‑intercept: (0, −3)
- x‑intercept: set y = 0 ⇒ 0 = 2x − 3 ⇒ x = 1.5, so (1.5, 0)
- Sample points: (−2, −7), (−1, −5), (0, −3), (1, −1), (2, 1), (3, 3)

That line is the graph of y = 2x − 3.