Question

Write the equation of the line that passes through the points (2 , -1) and has a slope of - 3​

Answer 1

y=-3x+5

Explanation:

y=mx+b

m=slope or gradient (=-3)

y=-3x+b

Add your points

(2, -1)

-1=(-3 x 2)+b

-1= -6+b

-1+6=b

b=5

y=-3x+5

Answer 2

`\boxed {\boxed {\sf y= -3x+5}}`

Explanation:

We are asked to find the equation of the line that passes through the point (2, -1) and has a slope of -3.

We are given a point and the slope, so we can use the point-slope formula.

`y-y_1=m(x-x_1)`

In this formula, m is the slope and (x₁, y₁) is the point the line passes through.

The line has a slope of -3 and passes through (2, -1).

• m= -3
• x₁= 2
• y₁= -1

Substitute the values into the formula.

`y--1= -3 (x-2)`

`y+1= -3 (x-2)`

Distribute the -3 on the right side. Multiply each term inside the parentheses by -3.

`y+1 = (-3*x) + (-3*-2)`

`y+1=(-3x) + (6)`

`y+1=-3x+6`

Subtract 1 from both sides of the equation to isolate the variable y.

`y+1-1=-3x+6-1`

`y=-3x +5`

The equation of the line is y= -3x+5.