Question

Find the equation of the line shown.

Answer 1

`\displaystyle y=(1)/(2)x-3`

Explanation:

Equation of a line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

`\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The graph of the picture shows two clear points (-4,-5) and (0,-3). We'll use them to find the required equation:

`\displaystyle y-(-5)=(-3-(-5))/(0-(-4))(x-(-4))`

Operating:

`\displaystyle y+5=(-3+5)/(0+4)(x+4)`

`\displaystyle y+5=(2)/(4)(x+4)`

Simplifying the fraction:

`\displaystyle y+5=(1)/(2)(x+4)`

Multiplying:

`\displaystyle y+5=(1)/(2)x+2`

Solving for y:

`\boxed{\displaystyle y=(1)/(2)x-3}`