Question

Find the equation of the line passing through the points (-5,-9) and (4,7)

Answer 1

`y=(16)/(9)x-(1)/(9)`

Explanations:

The formula for calculating the equation of a line is expressed as:

y = mx + b

where:

• m is the, slope, of the line

,

• b is the ,y-intercept

Given the coordinate points (-5,-9) and (4,7)

Determine the slope

`\begin{gathered} Slope=(y_2-y_1)/(x_2-x_1) \\ Slope=(7-(-9))/(4-(-5)) \\ Slope=(7+9)/(4+5) \\ Slope=(16)/(9) \end{gathered}`

Determine the y-intercept of the line

Recall that y = mx + b

`\begin{gathered} 7=(16)/(9)(4)+b \\ 7=(64)/(9)+b \\ b=7-(64)/(9) \\ b=-(1)/(9) \end{gathered}`

Determine the required equation

`\begin{gathered} y=mx+b \\ y=(16)/(9)x+(-(1)/(9)) \\ y=(16)/(9)x-(1)/(9) \end{gathered}`