Question

Find the equation in slope-intercept form that describes a line through (4, –2) with slope –3

Answer 1

Answer:
`y=-3x+10`

Explanation:

The equation of a line in intercept form:
`y=mx+c`

The equation of a line passing through (a,b) and has slope m is given by :_

`(y-b)=m(x-a)`

Similarly, the equation in slope-intercept form that describes a line through (4, -2) with slope -3 will be :_

`(y-(-2))=-3(x-4)\\\\\Rightarrow\ y+2=-3x+12\\\\\Rightarrow\ y=-3x+12-2\\\\\Rightarrow\ y=-3x+10\ \ \text{In intercept form}`

Hence, the equation in slope-intercept form that describes a line through (4, -2) with slope -3 =
`y=-3x+10`

Answer 2

y = - 3x + 10

Explanation:

The equation of a line in slope- intercept form is

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

here slope m = - 3, hence

y = - 3x + c ← is the partial equation

To find c substitute (4, - 2) into the partial equation

- 2 = - 12 + c ⇒ c = - 2 + 12 = 10

y = - 3x + 10 ← equation of line