11 Here is a table of values for the equation \(\quad y = 3x + 1\)
\(x\)
1
2
3
4
\(y\)
4
7
10
13
(a) Draw the graph of \(\quad y = 3x + 1 \quad\) for values of \(x\) from 1 to 4 [2 marks]
(b) Work out the value of \(y\) when \(\; x = 2.5\) [2 marks]
Mark scheme (a)
Answer
Mark
Comments
All 4 points plotted correctly with a straight line joining them
B2
\(\pm\)\(\dfrac{1}{2}\) square B1 at least two correct points plotted mark intention for straight line
Additional guidance
Ignore additional or incorrect points for B2 or B1
Ignore any line or curve extended outside the range
The correct position of the line implies correctly plotted points
Mark scheme (b)
Answer
Mark
Comments
Alternative method 1: uses the graph
Vertical line from \(x = 2.5\) to their straight line
M1
\(\pm\)\(\dfrac{1}{2}\) square implied by mark at correct point on graph or on vertical axis
their 8.5
A1ft
\(\pm\)\(\dfrac{1}{2}\) square ft their straight line graph if at least B1 awarded in (a)
Alternative method 2: substitutes into the equation
\(3 \times 2.5 + 1\)
M1
oe
8.5
A1
Alternative method 3: uses values from the table
\(\dfrac{7 + 10}{2}\)
M1
oe eg \(\dfrac{4 + 7 + 10 + 13}{4}\)
8.5
A1
Additional guidance
Alternative method 1 – must have a line in part (a)
Alternative method 1 A vertical line from the \(x\)-axis does not need to be drawn if the reading from the graph is correct within tolerance for their graph
