Question

Work out the equation of the line

Answer 1

Hi there!

We're given the following information:

• Slope (gradient) = ¹/₂
• Point = (4,2)

With this information, we can go ahead and plug the data into the point slope equation: y - y₁ = m(x - x₁).

Plug in 1/2 for m, and (4,2) for x1 and y1:

`\sf{y-y_1=m(x-x_1)}`

`\sf{y-(-2)=(1)/(2)(x-4)}`

`\sf{y+2=(1)/(2)(x-4)}`

`\sf{y+2=(1)/(2)x-2}\\\sf{y=(1)/(2)x-2-2}\\\\\sf{y=(1)/(2)x-4}`

Hence, y = 1/2x - 4.

I hope that helps! :)

Answer 2

Explanation:

Hi there!

According to the question;

The gradient of line is 1/2 and passes through the point (4,-2).

Since, It has one point and gradient we use one point formula to find the equation of the line.

Note:

One point formula: (y-y1) = m (x-x1)

(4,-2) = (x1,y1)

So, using this formula we get;

(y+2) = 1/2(x-4)

Multiply both sides by 2.

2(y+2) = (1/2)*2(x-4)

2y+4 = x-4

Take 2y+4 in right side

0 = x-4 - (2y+4)

Therefore, x-2y-8 = 0 is the required equation.

Hope it helps!