Mathematics

Problem

State the gradient and

y

-intercept of the line with equation: a. a

y = 3x + 7

b. b

y = -2x - 5

c. c

y = \frac{2}{3}x - \frac{1}{3}

d. d

y = 11 - 4x

e. e

y = -6 - x

f. f

y = \frac{9}{5} - \frac{6}{5}x

g. g

y = \frac{7x + 2}{9}

h. h

y = \frac{2x - 3}{6}

i. i

y = \frac{3 - 5x}{8}

Intuitive explanation

The key to reading a line's equation is recognizing its slope-intercept form $y = mx + b$ , where $m$ tells you the steepness (gradient) and $b$ tells you where the line crosses the $y$ -axis. If your equation isn't already in this form, rearrange it algebraically to isolate $y$ on one side—then the numbers fall right out.

Intuitive explanation

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