Question

In the given diagram, the line AB cuts the y-axis at the point C(10, 2) and passes through the point D(-3,-4). Find the slope and equation of the line CD.

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Answer 1

y = 2x + 2

Explanation:

To find the slope (gradient), use the formula:
`m=(y_2-y_1)/(x_2-x_1)`

where
`m` is the slope and
`(x_1, y_1)` and
`(x_2, y_2)` are the points C and D:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-4-2)/(-3-0)=2`

By inspection, we can see that the y-intercept is 2.

So using the equation of a straight line
`y=mx+c` where
`m` is the slope and
`c` is the y-intercept, the equation of the line CD is:

`y=2x+2`