Question

Graph a line that contains the point (6,-5) and has a slope of - 2/3

Answer 1

Answer:

The equation of line with slope $\dfrac{-2}{3}$  and passing through points ( 6 , - 5 ) is

y = ( $\dfrac{-2}{3}$ )x - 1   and graph shown

Step-by-step explanation:

Given as :

The points on the line is (6 , - 5)

The slope is m =  $\dfrac{-2}{3}$

Now, The equation of line with slope $\dfrac{-2}{3}$ and passing through points ( 6 , - 5) is

y = m x + c is the standard line equation

Now , satisfying the points

So, - 5 = ( $\dfrac{-2}{3}$ ) × 6 + c

or, - 5 = $\frac{-2\times 6}{3}$  + c

Or, - 5 = - 4 +  c

Or, c = - 5 + 4

∴  c = - 1

So, The equation of line with slope $\dfrac{-2}{3}$  and passing through points ( 6 , - 5 )

y = ( $\dfrac{-2}{3}$ ) × x - 1

Now, Plotting the line on graph

For x = 0 , y = 0 - 1 = -1

For , y = 0 , x = $\dfrac{-3}{2}$

So, points as ( 0 , - 1) and ( $\dfrac{-3}{2}$ , 0)

Hence , The equation of line with slope $\dfrac{-2}{3}$  and passing through points ( 6 , - 5 ) is y = ( $\dfrac{-2}{3}$ )x - 1    and graph shown Answer