Question

Which is an equation of the line with slope –3 and passes through (2, –1)?

a)

y = 5x – 3


b)

–3x + y = 5


c)

y = –3(x + 5)


d)

3x + y = 5

Answer 1

Answer: Option d.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

In this case we know that the slope of the line is:

`m=-3`

Knowing that it passes through the point (2, -1), we can substitute the coordinates into
`y=mx+b` and solve for "b":

`-1=-3(2)+b\\\\-1+6=b\\\\b=5`

Therefore, the equation of this line in Slope-Intercept form is:

`y=-3x+5`

Written in Standard form, this is:

`3x+y=5`

Answer 2

d) 3x + y = 5

Explanation:

The standard equation of a line with slope and a point is given by:

y = mx + b

We know that

m=-3

Putting the value of slope

y = -3x+b

To find the value of b, we will put the point in the equation

-1 = (-3)(2)+b

-1 = -6 + b

-1+6 = b

b = 5

Putting the values of b and m in standard equation

y = -3x+5

Can also be written as:

3x+y = 5

Hence,

Option d: 3x + y = 5 is the correct answer ..