Question

What is the y-intercept of the line that passes through the point (4,-9) with a slope of -1/2

Answer 1

The y-intercept b for the derived equation is;

`b=-7`

Step-by-step explanation:

Given that the line passes through the point (4,-9) and has a slope of -1/2;

`\begin{gathered} \text{slope m=-}(1)/(2) \\ \text{ point (4,-9)} \end{gathered}`

Applying the point-slope form of linear equation;

`y-y_1=m(x-x_1)`

substituting the slope and the given point;

`\begin{gathered} y-(-9)=-(1)/(2)(x-4) \\ y+9=-(1)/(2)x+(4)/(2) \\ y+9=-(x)/(2)+2 \\ y=-(x)/(2)+2-9 \\ y=-(x)/(2)-7 \end{gathered}`

Comparing it to the slope intercept form of linear equation;

`y=mx+b`

where;

m = slope

and b = y-intercept

Therefore, the y-intercept b for the derived equation is;

`b=-7`