Question

Write the equation of the line that passes through the points (-8,7) and (2, -7).Put your answer in fully simplified point-slope form, unless it is a vertical orhorizontal line.

Answer 1

Answer: y = -7/5x -21/5

Explanations:

GIVEN POINTS

• ( x1;y1 ) = ( -8;7)

,

• (x2;y2 ) = (2;-7)

(i) Calculate the Slope -substitude given point into the slope formula below:

$\begin{gathered} Slope\text{ \lparen m\rparen = }\frac{y_2-y_1}{x_2-x_1} \\ \text{ = }\frac{-7\text{ -7}}{2-(-8)} \\ \text{ =}\frac{-14}{10} \\ \text{ =-}\frac{7}{5} \\ \text{ } \end{gathered}$

Therefore , the slope = -7/5

Our equation will follow the standard equation of a straight line :

$\begin{gathered} y\text{ = mx +c } \\ where\text{ m = -7/5 and c is the y intercept } \end{gathered}$

(ii) Calculate the y - intercept

• Now, our equation looks like this ,: y = -7/5x +c

,

• Subtitute any of the given point and solve for point c , lets choose point (, 2;-7),

$\begin{gathered} y\text{ = -}\frac{7}{5}\text{ + c ....at point \lparen 2;-7\rparen } \\ -7\text{ = -}\frac{7}{5}(2)\text{ +c } \\ -7\text{ = }\frac{-14}{5}\text{ +c} \\ -7\text{ +}\frac{14}{5}\text{ = C } \\ \therefore C\text{ = -21/5} \end{gathered}$

This means that the C value = -21/5

Our final equation of the line that passes through the given points will be :

$y\text{ = }\frac{-7}{5}x-\frac{21}{5}$