Grade 10 Maths · Functions

Calculate gradient between two points

Find how steep a line is using (y₂ − y₁) ÷ (x₂ − x₁) (for example from (1; 2) to (3; 8) the gradient is 6 ÷ 2 = 3).

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Straight line graphs grade 9: Gradient Part 1Kevinmathscience

Analytical Geometry Grade 10: Gradient formulaKevinmathscience

Analytical Geometry Gradient formula Grade 10 MathsMiss Martins Maths and Science

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Question 6.3 · May/June 2024 · Paper 1 · National (DBE) · 2 marks

The graphs of

f (x) = x^{2} - 2 x - 3

and

g (x) = m x + c

are drawn below. D and E are the

x

-intercepts and P is the

y

-intercept of

f

. The turning point of

f

is T

(1; - 4)

. The graphs of

f

and

g

intersect at P and E. Diagram for this question

6.3 Determine the equation of g.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: calculate gradient between two points

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3. Question 6.2 · November 2024 · Paper 1 · National (DBE) · 3 marks
In the diagram below, the graphs of $f (x) = - x^{2} + 4 x + 5$ and $g$ , a straight line, are drawn. $C (3; 8)$ is a point of intersection of $f$ and $g$ . $E H$ is drawn parallel to the y-axis, with $E$ a point on $f$ and $H$ a point on $g$ .
6.2 Show that the equation of the line through $A$ and $C$ is given by $g (x) = 2 x + 2$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Determine coordinates of A (x-intercept) $x^{2} - 4 x - 5 = 0$
  $(x - 5) (x + 1) = 0$
  $x = 5$ or $x = - 1$
  Therefore $A (- 1; 0)$
  1 mark · Find the x-intercepts
2. ✓
  Calculate gradient of AC $m = \frac{8 - 0}{3 - ( - 1 )} = \frac{8}{4}$
  $m = 2$
  1 mark · Calculate gradient between two points
3. ✓
  Determine equation of line $y - 0 = 2 (x + 1)$
  $y = 2 x + 2$
  1 mark · Find the equation of a line
4. Question 1.4 · June 2024 · Paper 2 · Provincial · 2 marks
$PQRS$ is a quadrilateral with vertices $P (- 5; 0)$ , $Q (0; t)$ , $R (3; - 2)$ and $S (- 2; - 5)$ .
$P$ is on the x-axis and $Q$ is on the y-axis.
1.4 Determine the gradient of $PQ$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution into the gradient formula $m_{PQ} = \frac{3 - 0}{0 + 5}$
  1 mark · Calculate gradient between two points
2. ✓
  Gradient of PQ $m_{PQ} = \frac{3}{5}$
  1 mark · Calculate gradient between two points
5. Question 1.3 · June 2024 · Paper 2 · Provincial · 3 marks
In the figure below, $A (- 5; 2)$ and $B (4; - 2)$ are points on a line segment AB.
1.3 Determine the gradient of line AB.(3)
Show the memo (2 ticks)Memo
1. ✓
  Apply gradient formula $m_{A B} = \frac{y _{A} - y _{B}}{x _{A} - x _{B}}$
  $= \frac{2 - ( - 2 )}{- 5 - 4}$
  2 marks · Calculate gradient between two points
2. ✓
  Calculate gradient $= \frac{4}{- 9}$
  1 mark · Calculate gradient between two points
6. Question 1.3 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, $A (- 2; 2)$ , $B (- 4; - 6)$ , $C (4; - 2)$ and $E (6; y)$ are the vertices of a quadrilateral with $A E ∣∣ BC$ . $D$ lies on $BC$ such that $A D ⊥ BC$ and $A C$ is drawn. $M (x; 2)$ is a point on line $EC$ .
1.3 Calculate the gradient of $BC$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into gradient formula $m_{BC} = \frac{- 2 - ( - 6 )}{4 - ( - 4 )}$
  1 mark · Calculate gradient between two points
2. ✓
  Simplify $m_{BC} = \frac{4}{8} = \frac{1}{2}$
  1 mark · Calculate gradient between two points

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