Question

DUE TOMORROW! 30 POINTS

20. Consider a line passing through (2,5) with a slope of ¾ . Write its equation. What is its y-intercept?
21. Write the equation for a line parallel to the line from #20 passing through (5,1). Now write the equation for a line perpendicular to the same line, through the same point.

Answer 1

20) y = 3/4x + 3 1/2

21) Parallel: y = 3/4 x - 2 3/4

Perpendicular: y =
`(-4)/(3 )` x + 7
`(2)/(3)`

Explanation:

20)

y = mx + b

y = __x + ___ We need to find the slope that the y-intercept. We are given the slope 3/4. We will you the x and y values from the point (2,5) to find the y intercept. Use 5 for y and 2 for x

y = mx + b

5 = 2(3/4) + b

5 = 3/2 + b Subtract 3/2 from both sides

5 - 3/2 = 3/2 -3/2 +b

`(10)/(2)` -
`(3)/(2)` = b

`(7)/(2)` or 3
`(1)/(2)`

y = 3/4x + 3 1/2

21)

Parallel slopes are equal so the slope will be 3/4. Now we will use the x and y values from the point (5,1) to find the y-intercept. We will use 1for y and 5 for x

y = mx + b

1 = 5(3/4) +b

1 = 15/4 + b Subtract 15/4 from both sides.

`(4)/(4)` -
`(15)/(4)` =
`(15)/(4)` -
`(15)/(4)` + b

`(-11)/(4)` or - 2
`(3)/(4)`

y = 3/4 x - 2 3/4

Perpendicular slopes or the opposite reciprocals. So the slope of the reciprocal equations would be
`(-4)/(3)`. We would still use the x and y values from the point (5,1)

1 = -4/3(5) + b

1 =
`(-20)/(3)` + b Add 20/3 to both sides

`(3)/(3)` +
`(20)/(3)` =
`(-20)/(3)` +
`\frac{20}3}` + b

`(23)/(3)` or 7 2/3

y =
`(-4)/(3 )` x + 7
`(2)/(3)`

Helping in the name of Jesus.