Question

Diagram shows two perpendicular straight lines,OB and CBD,drawn on a Cartesian plane.

find
(a)the equation of the straight line CBD
(b)the-x intercept of the straight line DQ

Answer 1

Answer: (a) y = -3x + 10

`\bold{(b)\x=\bigg((10)/(3),0\bigg)}`

Explanation:

The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.

Step 1: Find the slope of OB using the formula:
`m=(y_2-y_1)/(x_2-x_1)`

(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)

`m=(1-0)/(3-0) = (1)/(3)`

Step 2: Find the slope of CD (opposite and reciprocal of OB)

`m = (1)/(3)\qquad m_\perp=-\bigg((3)/(1)\bigg) = -3`

Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)

(x₁, y₁) = (3, 1) because it is the point the line will pass through

y - 1 = -3(x - 3)

y - 1 = -3x + 9 distributed -3 into (x - 3)

y = -3x + 10 added 1 to both sides

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The x-intercept of DQ is the same x-intercept as CD. The x-intercept is when y = 0

y = -3x + 10

0 = -3x + 10

-10 = -3x subtracted 10 from both sides

`(10)/(3)=x` divided both sides by -3