Linear functions are functions of the form f(x) = mx + c and their graphical representation is a straight line.
m is the slope or the gradient of the line; it represents the steepness of the line.
c is the y - intercept; where the line crosses the y - axis
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If the straight line slopes upwards when moving from left to right, then the line has a positive slope or gradient. Equation of line: y = mx + c, where m > 0 Domain: R (the real numbers set) Range: R (the real numbers set) |
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If the straight line slopes downwards when moving from left to right, then the line has a negative slope or gradient. Equation of line: y = mx + c, where m < 0 Domain: R (the real numbers set) Range: R (the real numbers set) |
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If the straight line is horizontal, then the line has a zero slope or gradient, m. Equation of line: y = c, with m = 0 Domain: R (the real numbers set) Range: {c} |
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If the straight line is vertical, then the line has an undefined slope or gradient, m. Equation of line: x = a, with m → ∞ Domain: {a} Range: R (the real numbers set)
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x-intercept occurs when y = 0 0 = mx + c
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y-intercept occurs when x = 0 y = m × 0 + c y = c |
