Question

The slope and one point on the line are given. Find the equation of the line (in slope-intercept form).(1/4, -4) ; m = -3 y=

Answer 1

y = -3x - 13/4

Explanation

Equation of a line in slope-intercept form

`y=mx+b`

where m is the slope and (0, b) is the y-intercept.

Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:

`\begin{gathered} -4=(-3)\cdot(1)/(4)+b \\ -4=-(3)/(4)+b \\ -4+(3)/(4)=-(3)/(4)+b+(3)/(4) \\ -(13)/(4)=b \end{gathered}`

Substituting into the general equation with m = -3 and b = -13/4, we get:

`\begin{gathered} y=(-3)x+(-(13)/(4)) \\ y=-3x-(13)/(4) \end{gathered}`