Question

1) Write the equation of the line passing through point P with slope m, if

a) P(1,4) and m = 3

c) P (3,0) and m = −1

b) P(-1,-2) and m = 4

d) P(0,0) and m = -5

Answer 1

a) y - 4 =3(x - 1)

b) y + 2 = 4(x+ 1)

c) y = -(x - 3)

d) y = -5x

Explanation:

You did not say which form, so I put them in the point-slope form of a line that follows the pattern:

y -
`y_(1)` = m( x -
`x_(1)`)

Answer 2

see explanation

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (1, 4 ) into the partial equation

4 = 3(1) + c = 3 + c ( subtract 3 from both sides )

1 = c

y = 3x + 1 ← equation of line

(b)

given m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, - 2 ) into the partial equation

- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )

2 = c

y = 4x + 2 ← equation of line

(c)

given m = - 1 , then

y = - x + c ← is the partial equation

to find c substitute (3, 0 ) into the partial equation

0 = - 3 + c ( add 3 to both sides )

3 = c

y = - x + 3 ← equation of line

(d)

given m = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (0, 0 ) into the partial equation

0 = - 5(0) + c = 0 + c ⇒ c = 0

y = - 5x ← equation of line