Additional Mathematics – Straight-line graphs | e-Consult
Straight-line graphs (1 questions)
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Answer 3
- Rewrite in slope‑intercept form:
2x – 5y + 10 = 0 ⇒ 5y = 2x + 10 ⇒ y = (2/5)x + 2.
Hence the gradient m = 2/5.
For the x‑intercept set y = 0 in the original equation:
2x + 10 = 0 ⇒ x = ‑5 Thus the x‑intercept is (‑5, 0).
For the y‑intercept set x = 0:
‑5y + 10 = 0 ⇒ y = 2 Thus the y‑intercept is (0, 2).
Intersection with y = x: substitute y = x into 2x – 5y + 10 = 0:
2x – 5x + 10 = 0 ⇒ ‑3x + 10 = 0 ⇒ x = 10/3 Since y = x, y = 10/3. The point of intersection is (10/3, 10/3).