Question

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

Answer 1

The slope-point form of a line:

`y-y_0=m(x-x_0)`

We have

`m=-(1)/(4)\\\\\left(-2,\ -(9)/(2)\right)\to x=-2,\ y=-(9)/(2)`

Substitute

`y-\left(-(9)/(2)\right)=-(1)/(4)(x-(-2))\\\\y+(9)/(2)=-(1)/(4)(x+2)`

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept

Solve for y:

`y+(9)/(2)=-(1)/(4)(x+2)\qquad|\text{use distributive property}\\\\y+(9)/(2)=-(1)/(4)x-(1)/(2)\qquad|\text{subtract}\ (9)/(2)\ \text{from both sides}\\\\y=-(1)/(4)x-(10)/(2)\\\\y=-(1)/(4)x-5`

Amswer: y-intercept = -5.