Question

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Answer 1

The question states that there are 2 points with coordinates: (5,7) and (10,14) through which a straight lines passes through. We are asked to find the slope which this line makes with the x-axis.

To determine the value of slope, we can use the Two Point Form of a Straight line. The formula for Two Point form is:

⇒ ( y₂ - y₁ / x₂ - x₁ ) = ( y - y₁ / x - x₁ )

Here, y₂ and y₁ are the y coordinates of the two given points while x₂ and x₁ are the x coordinates of the two given points.

Substituting the values we get,

⇒ ( 14 - 7 / 10 - 5 ) = ( y - 7 / x - 5 )

⇒ 7/5 = ( y - 7 / x - 5 )

⇒ 7/5 × ( x - 5 ) = y - 7

⇒ 7x/5 - 35/5 = y - 7

⇒ 7x/5 - 7 = y - 7

Cancelling the 7 on both sides we get,

⇒ 7x/5 = y

Now comparing this equation with y = mx we get,

⇒ y = (7/5) x

Hence on comparing we get, m = 7/5 which is the required slope.

(In decimals the slope is 1.4).

Hope it helped!

Answer 2

Answer:

Well here line is passing through origin

Step-by-step explanation:

So , y and x are proportional coordinates where proportionality constant denotes slope

As line is passing through (5,7)

So, Slope simply becomes

( y coordinate)/( respective x coordinate)

= 7/5

Or

See in ∆OAB

tan<OAB =>AB/OB = 7/5

Note : No need to find slope using 2 coordinates as y and x are proportional that is one coordinate is origin So its simply becomes ratio of y coordinate to x coordinate

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