Question

sophia is designig a logo with three lines,y, m, and n. Line m passes through point (-2, -1) and is perpendicular to the graoh of y=-2/3 x +6. line n is parallel to line m and passes through the point (4, -3). what is the equation in slope-intercept form of linen?

Answer 1

y = 3/2x - 9

Explanation:

Finding equation of line m

• ⊥ to the line y = -2/3x + 6
• new slope = -(-3/2) = 3/2
• Passes through the point (-2, -1)
• y + 1 = 3/2(x + 2)
• y + 1 = 3/2x + 3
• y = 3/2x + 2

Equation of line n

• Parallel ⇒ slope is same = 3/2
• Passes through the point (4, -3)
• y + 3 = 3/2(x - 4)
• y + 3 = 3/2x - 6
• y = 3/2x - 9

Answer 2

`\textsf{Equation of line n}:\quad y=\frac32x-9`

Explanation:

Equation of line m

If two lines are perpendicular to each other, the product of their slopes will be -1.

The slope of the line
`y=-\frac23x+6` is
`-\frac23`

Therefore, the slope of the line m is:

`\implies m * -\frac23=-1`

`\implies m=\frac32`

If line m passes through point (-2, -1), then the equation of line m is:

`\implies y-(-1)=\frac32(x-(-2))`

`\implies y+1=\frac32(x+2)`

`\implies y=\frac32x+2`

Equation of line n

If line n is parallel to line m, then they will have the same slope.

Therefore, slope of line n is
`\frac32`

If line n passes through point (4, -3), then the equation of line n is:

`\implies y-(-3)=\frac32(x-4)`

`\implies y+3=\frac32x-6`

`\implies y=\frac32x-9`