Question

A line passes through the origin and the point (1, 2). Use this information to answer question 13 and 14

13. What is the gradient of the line?
14. Find the y-coordinate of the line when x = 4 ​

Answer 1

Given to us that:–

• a line passes through the origin and the point (1,2)

To find:–

• Gradient = ??

By using the gradient formula,

Gradient (m) of a line

`\underbrace{\bf{m=(y_2-y_1)/(x_2-x_1)}}_(gradient)`

The two points are (0,0) and (1,2)

By substituting the known values,

`\bf{m=(2-0)/(1-0)}`

`\bf{m=(2)/(1)}`

`\bf{m=2}`

Henceforth, Gradient = 2

Let's find the y-intercept now . We know that x = 4 so we substitute it into the line's equation, which is :

y = 4x + c

➱ y - > y-coordinate

➱ m - > slope

➱ x - > x-coordinate

➱ c - > y-intercept

Substitute the point into the equation:-

➱
`\bf{2=4(1)+c}`

➱
`\bf{2=4+c}`

➱
`\bf{2-4=c}`

➱
`\bf{-2=c}`

Now that we know the y-intercept, we can find the y-coordinate :

➱
`\bf{y=4\cdot4 -2}`

➱
`\bf{y=16-2}`

➱
`\bf{y=14}`

✯ Henceforth, The y-coordinate is y = 14