Question

Can anyone help me solve 23, 24?

Answer 1

Problem 23)
`y=3x+6`

Problem 24)
`y=-(1)/(3)x-5`

Explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

`A(0,2)\ B(3,1)`

Substitute the values

`m=(1-2)/(3-0)`

`m=-(1)/(3)`

step 2

Problem 23

we know that

If two lines are perpendicular then the product of its slopes is equal to minus 1

so

`m1*m2=-1`

Find the slope of the line

we have

`m1=-(1)/(3)`

substitute in the equation and solve for m2

`(-(1)/(3))*m2=-1`

`m2=3`

with the slope m2 and the point
`(0,6)` find the equation of the line

Remember that

The equation of the line in slope intercept form is equal to

`y=mx+b`

we have

`m=3`

`b=6` -----> the given point is the y-intercept

substitute

`y=3x+6`

step 3

Problem 24

we know that

If two lines are parallel, then its slopes are the same

so

with the slope m1 and the point
`(0,-5)` find the equation of the line

The equation of the line in slope intercept form is equal to

`y=mx+b`

we have

`m=-(1)/(3)`

`b=-5` -----> the given point is the y-intercept

substitute

`y=-(1)/(3)x-5`