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Mathematics: AI HL

Functions

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Mathematics: AI HL

Available time 20 Minute(s)

The equation of a line is given.

Functions

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Available time 20 Minute(s)

01. Question

Level Easy

Maximum Mark 6

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The equation of a line $L_{1}$ is $y - 5 x + 7 = 0$ .

(a). For the line $L_{1}$ find:

(i) the x-intercept:

[Marks: 1]

(ii) the gradient.

[Marks: 1]

A second line, $L_{2}$ , intersects the y-axis at $P (0, 3)$ and is paralle’ to $L_{1}$ .

(b). Find the equation of $L_{2}$ . Give your answer in the form $y = m x + c$ .

[Marks: 1]

A third line, $L_{3}$ , passes through the point $Q (5, 3)$ and is perpendicular to $L_{1}$ .

(c). Find the gradient of the line $L_{3} .$

[Marks: 1]

(d). Find the equation of $L_{3}$ , giving your answer in the form $a x + b y + d = 0$ . where $a, b, d \in ℤ$

[Marks: 2]

End Test