Question

Complete the equation of the line through (-7,-3) and (-2,4)

Answer 1

If one line passes through the points (x₁, y₁) and (x₂, y), the slope of the line can be calculated using the formula:

`m=(y_2-y_1)/(x_2-x_1)...(1)`

Additionally, the equation can be expressed in point-slope form as:

`y-y_2=m(x-x_2)...(2)`

From the problem, we identify:

`\begin{gathered} (x_1,y_1)=(-7,-3) \\ \\ (x_2,y_2)=(-2,4) \end{gathered}`

Then, we calculate the slope of the line using (1):

`m=(4-(-3))/(-2-(-7))=(4+3)/(-2+7)=(7)/(5)`

Finally, we find the equation of the line using (2):

`\therefore y-4=(7)/(5)(x+2)`