Question

Writing the equation of the line through two given points(1,-3) (5,-1). y=mx+b form

Answer 1

Given points (1,-3) and (5,-1).

Since the slope of the line passing through two points

`(x_1,y_1)(x_2,y_2)`

The slope of the equation is

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(-1-(-3))/(5-1) \\ m=(2)/(4) \\ m=(1)/(2) \end{gathered}`

Therefore, the slope of the line is 1/2.

Now, use the slope and the point (1,-3) to find the y-intercept.

`\begin{gathered} y=mx+c \\ -3=(1)/(2)*1+c \\ c=-3-(1)/(2) \\ c=-(-7)/(2) \end{gathered}`

Write the equation in slope-intercept form as

`\begin{gathered} y=mx+c \\ y=(1)/(2)x-(7)/(2) \end{gathered}`