← ACARA Digital Technologies Years 9–10

SLOPE and INTERCEPT for a prediction equation

SLOPE gives m and INTERCEPT gives c of the best-fit line, so a prediction can be written as y = m*x + c. Both functions take known_y first, then known_x.

Part of: ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 47

Understanding SLOPE and INTERCEPT for a prediction equation in ACARA Digital Technologies Years 9–10

What it does: The cell formula copies the equation y = m*x + c: slope times x, plus the intercept. The y range (sales) goes first and the x range (temperature) goes second, which is the INTERCEPT order. SLOPE takes known_y first, then known_x. Here y is in B2:B9 and x is in A2:A9, so the y range comes first. INTERCEPT gives c, where the line crosses the y-axis (x = 0). The rise in y for each 1 step in x is the slope, m. Absolute references with $ lock the cells holding m and c. Copying the formula down only changes the x cell reference.

Common mistakes: The equation y = m*x + c needs the slope (m, in E1) multiplied by x and the intercept (c, in E2) added. The formula swapped them. It should be =E1*F1+E2. In y = m*x + c the slope m is multiplied by x, not added to it. The line should be =E1*F1+E2.

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This module's key terms are also in a printable crossword (Modules 378–412) and word search (Modules 333–412).

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Learning
Duo
Which formula returns the gradient (m) of the best-fit line when the y values are in B2:B9 and the x values are in A2:A9?
=SLOPE(A2:A9,B2:B9)=SLOPE(B2:B9,A2:A9)
Matches
=SLOPE(A2:A9,B2:B9) where A is x (hours studied) and B is y (test mark)
↓
The arguments are the wrong way round. SLOPE needs known_y first, so the marks (B2:B9) must come before the hours (A2:A9).
Applying
Meanings
Term
SLOPE and INTERCEPT
Meaning
SLOPE gives m and INTERCEPT gives c of the best-fit line, so a prediction can be written as y = m*x + c. Both functions take known_y first, then known_x.
Practice
=SLOPE(C2:C8,B2:B8)*30+INTERCEPT(C2:C8,B2:B8)
Testing
Gaps
=(B2:B9,A2:A9)
Check Answer
Spots
2E2: =INTERCEPT(C2:C9,B2:B9)
3E3: =E2*F1+E1

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Quick Questions

1. Which formula returns the gradient (m) of the best-fit line when the y values are in B2:B9 and the x values are in A2:A9?
A. =SLOPE(A2:A9,B2:B9)
B. =SLOPE(B2:B9,A2:A9) ✓
SLOPE takes known_y first, then known_x. Here y is in B2:B9 and x is in A2:A9, so the y range comes first.
2. Which formula returns the y-intercept (c) of the best-fit line when the y values are in B2:B9 and the x values are in A2:A9?
A. =INTERCEPT(B2:B9,A2:A9) ✓
B. =INTERCEPT(A2:A9,B2:B9)
INTERCEPT uses the same order as SLOPE: known_y first, then known_x.
3. A best-fit line has SLOPE = 2.5 and INTERCEPT = 10. Which equation is the prediction equation?
A. y = 2.5*x + 10 ✓
B. y = 10*x + 2.5
The prediction equation is y = m*x + c. The slope m is multiplied by x, and the intercept c is added on.
4. What does INTERCEPT tell you about the best-fit line?
A. How much y rises for each 1 increase in x
B. The predicted y value when x is 0 ✓
INTERCEPT gives c, where the line crosses the y-axis (x = 0). The rise in y for each 1 step in x is the slope, m.
5. The slope in cell E1 is 3 and the intercept in cell E2 is 5. Which formula predicts y when x is in A2?
A. =E1*A2+E2 ✓
B. =E1+A2*E2
This is y = m*x + c written in cells: slope times x, plus the intercept. The other formula multiplies x by the intercept, which is wrong.

Match the Pairs

=SLOPE(B2:B9,A2:A9) → Returns m, the gradient of the best-fit line, using the y values in B2:B9 and the x values in A2:A9
=INTERCEPT(B2:B9,A2:A9) → Returns c, the value where the best-fit line crosses the y-axis (the predicted y when x is 0)
Once m is in E1 and c is in E2, a prediction for the x value in D2 is written as y = m*x + c → =E1*D2+E2
To get the intercept c of a line where sales are y (C2:C13) and temperature is x (B2:B13) → =INTERCEPT(C2:C13,B2:B13)
=SLOPE(A2:A9,B2:B9) where A is x (hours studied) and B is y (test mark) → The arguments are the wrong way round. SLOPE needs known_y first, so the marks (B2:B9) must come before the hours (A2:A9).
=E1+E2*D2 (trying to predict y from m in E1 and c in E2) → The equation is built incorrectly. It treats the intercept as the gradient, so m is not multiplied by x and c is multiplied instead.

Key Term

SLOPE and INTERCEPT
SLOPE gives m and INTERCEPT gives c of the best-fit line, so a prediction can be written as y = m*x + c. Both functions take known_y first, then known_x.

Fill in the Blanks

1. =SLOPE(B2:B9,A2:A9)
Hint: Type the function that returns m, the gradient of the best-fit line.
2. =INTERCEPT(B2:B9,A2:A9)
Hint: Type the function that returns c, where the best-fit line crosses the y-axis.
3. =SLOPE(B2:B9,A2:A9)
Hint: Known_y comes first. Type the range of y values, the ones being predicted, which sit in column B.
4. =E1*A12+E2
Hint: E1 holds the slope m and E2 holds the intercept c. Type the operator that multiplies m by x.
5. =E1*A12+E2
Hint: To finish y = m*x + c, type the cell reference that holds the intercept c. The slope m is in E1.

Spot the Error

Question 1
A E1: =SLOPE(C2:C9,B2:B9)
B E2: =INTERCEPT(C2:C9,B2:B9)
C E3: =E2*F1+E1
Line C — The equation y = m*x + c needs the slope (m, in E1) multiplied by x and the intercept (c, in E2) added. The formula swapped them. It should be =E1*F1+E2.
Question 2
A E1: =SLOPE(C2:C9,B2:B9)
B E2: =INTERCEPT(C2:C9,B2:B9)
C E3: =E1+F1+E2
Line C — In y = m*x + c the slope m is multiplied by x, not added to it. The line should be =E1*F1+E2.
Question 3
A E1: =SLOPE(B2:B9,D2:D9)
B E2: =INTERCEPT(D2:D9,B2:B9)
C E3: =E1*F1+E2
Line A — SLOPE takes known_y first, then known_x. The arguments were swapped, so the slope is for the wrong direction. It should be =SLOPE(D2:D9,B2:B9).
Question 4
A E1: =SLOPE(D2:D9,B2:B9)
B F1: 70
C E3: =INTERCEPT(B2:B9,D2:D9)
D E4: =E1*F1+E3
Line C — INTERCEPT also takes known_y first, then known_x. The ranges were swapped, which gives the intercept of the wrong line. It should be =INTERCEPT(D2:D9,B2:B9).
Question 5
A E1: =SLOPE(C2:C9,B2:B9)
B E2: =SLOPE(C2:C9,B2:B9)
C E3: =E1*F1+E2
Line B — E2 should hold c, the intercept, but SLOPE gives m again. The line should use =INTERCEPT(C2:C9,B2:B9).

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