Test: Graphing linear functions - Year 8 MCQ

This is a horizontal line - note that in both sets of coordinates the second numbers are the same.

Both sets of coordinates show the x axis figure of 0 and this means that the line must run up and down the y axis.

For the equation x = a, the x-coordinate is constant at a, resulting in a straight vertical line parallel to the y-axis. For example, x = 4 is a vertical line passing through x = 4 on the graph.

The equation x = 4 represents a vertical line where the x-coordinate is always 4. This line is parallel to the y-axis and located four units to the right of the y-axis.

Think of it this way: if y = 4 then x = 4, if y = -4 then x = -4.

In other words, whatever the first number in the coordinates, the second number will always be the same

Arithmetic sequences form linear functions when plotted against the term number. The points (1, 7), (2, 12), (3, 17), (4, 22) lie on the line y = 5x + 2, which has a positive slope of 5 and is straight.

Think of it this way: if y = 4 then x = -4, if y = -4 then x = 4.

In other words, whatever the first number in the coordinates, the second number will always be the same BUT with the opposite sign

In a linear sequence where each term increases by a constant difference (common difference of 3), the slope of the graph (y vs. term number) is equal to that difference. For example, the points (1,2), (2,5), (3,8) lie on y = 3x - 1, with slope 3.

Substitute x = 3 into the function f(x) = 2x + 1. Thus, f(3) = 2(3) + 1 = 6 + 1 = 7.

The y-intercept is the point where the line crosses the y-axis (x=0). Substituting x=0 into y = 2x + 3 gives y=3, so the point is (0, 3). This is a basic property of graphing linear functions in slope-intercept form (y = mx + b, where b is the y-intercept).