KJSEA 2025 Maths Q35 — Linear Graphs (Milk Sales y = 50x)

KJSEA 2025 Grade 9 Algebra

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The Question

“The money a farmer gets from selling milk is given by y = 50x, where x is the amount of milk in litres and y is the money received. Part A: complete the table of values for the equation. Part B: use the values to draw the graph of y = 50x.”

1

Understand the equation

The equation tells you that the money earned is always 50 times the number of litres sold. So for any value of x you simply multiply it by 50 to get y. This is the rule you use to fill every gap in the table.

y=50xy = 50x
2

Fill the missing table values

Work through each x value using the rule. When half a litre is sold, multiply 0.5 by 50 to get 25. When two litres are sold, multiply 2 by 50 to get 100. Those are the two missing entries in the table.

x=0.5⇒y=50×0.5=25x = 0.5 \Rightarrow y = 50 \times 0.5 = 25
x=2⇒y=50×2=100x = 2 \Rightarrow y = 50 \times 2 = 100

The missing values are 25 and 100.

3

Note the point at the origin

When no milk is sold, no money is earned. Putting x equal to zero gives y equal to zero, so the line must start at the origin. This anchors the graph in the bottom-left corner of the grid.

x=0⇒y=50×0=0x = 0 \Rightarrow y = 50 \times 0 = 0
4

Plot the points and join them

Mark each pair of values from the table as a point on the grid, using x across and y up. Then draw a single straight line through the plotted points and the origin with a ruler. Because the relationship is linear, all the points line up perfectly.

(0, 0), (0.5, 25), (2, 100)(0,\ 0),\ (0.5,\ 25),\ (2,\ 100)
5

Describe the line

The line rises steeply because the money increases by 50 for every extra litre. This constant rate of increase is the gradient of the line, and it equals the number in front of x in the equation.

gradient=50\text{gradient} = 50

Final Result

The missing table values are y = 25 (when x = 0.5) and y = 100 (when x = 2). The graph is a straight line passing through the origin with gradient 50.

Why this method works

The equation y = 50x is a direct proportion: y changes at a fixed rate of 50 for every unit increase in x, and it is zero when x is zero. Any relationship of this form always graphs as a straight line through the origin, because there is no constant added on to lift the line up or down. The number multiplying x is the gradient, so it controls how steeply the line climbs — here every extra litre adds another 50 shillings, giving a steep, even slope.

✓

Check a point not used for plotting: if x = 1, then y = 50 × 1 = 50, and reading the line at x = 1 does give y = 50.