What would be the linear equation for this function, & the graph?(X_1,Y_1)=(4,8), (X_2,Y_2)=(6,-9)

Question

What would be the linear equation for this function, and the graph?
$(X_{1}, Y_{1}) = (4, 8), (X_{2}, Y_{2}) = (6, - 9)$

Answer 1

Formula used:
Point-slope form of line:

(y_{2} - y_{1}) = m (x_{2} - x_{1})

So, by the Point-Slope form of line the equation of line is given below:

(- 9 - 8) = m (6 - 4)

- 17 = m \times 2

2 m = - 17

m = - \frac{17}{2}

Now

m = - \frac{17}{2}

and take any points to find the linear equation.

(x_{1}, y_{1}) = (4, 8) and m = - \frac{17}{2}

(y - y_{1}) = m (x - x_{1})

(y - 8) = - \frac{17}{2} (x - 4)

(y - 8) = \frac{- 17 x}{2} + 34

y = \frac{- 17 x}{2} + 34 + 8

y = \frac{- 17 x}{2} + 42

y = \frac{- 17 x + 84}{2}

2 y = - 17 x_{84}

So, the graph is given below:

Expert Answer