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Question
Draw the graph of a line 2x + 3y = 6. From the graph, find the slope and y-intercept of the line.
Solution
2x + 3y = 6
3y = 6 - 2x
y = `(6)/(3) - (2)/(3)x`
∴ y = `2 - (2)/(3)x`
When x = 3, y = `2 - (2)/(3)(3)` = 0
When x = -3, y = `2 - (2)/(3)(-3)` = 4
When x = 0, y = `2 - (2)/(3)(0)` = 2
| x | 3 | -3 | 0 |
| y | 0 | 4 | 2 |
Plotting the points (3, 0), (-3, 4) and (0, 2), we get line segment as shown in the figure.
∴ The y-intercept is 2.
Slope
= `"Change in y"/"Change in x"`
= `(2 - 0)/(0 - 3)`
= `(2)/(-3)`
∴ Slope
= `(-2)/(3)`.
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