Question

What is the equation of the line that passes through the point (6,-7) and has a slope of -3/2

Answer 1

The point-slope form:

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

We have the point (6, -7) and the slope m = -3/2. Substitute:

`y-(-7)=-(3)/(2)(x-6)\\\\\boxed{y+7=-(3)/(2)(x-6)}`

`y+7=-(3)/(2)(x-6)` use distributive property

`y+7=-(3)/(2)x+9` subtract 7 from both sides

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

`y=-(3)/(2)x+2` multiply both sides by 2

`2y=-3x+4` add 3x to both sides

`\boxed{3x+2y=4}`

Answer:

point-slope form:
`y+7=-(3)/(2)(x-6)`

slope-intercept form:
`y=-(3)/(2)x+2`

standard form:
`3x+2y=4`