Question

Graph the line with slope-2/3 passing through the point (-5, -4),

Answer 1

Answer:

The figure is attached down

Step-by-step explanation:

To graph a line you must have its equation

The form of the linear equation is y = m x + b, where

• m is its slope
• b is the y-intercept (y at x = 0)

∵ The slope of the line is  $-\frac{2}{3}$

∴ y = $-\frac{2}{3}$ x + b

- To find b substitute x and y in the equation by the coordinates

   of a point on the line

∵ The line passing through point (-5 , -4)

∴ x = -5 and y = -4

∵ -4 =  $-\frac{2}{3}$ (-5) + b

∴ -4 = $\frac{10}{3}$ + b

- Subtract  $\frac{10}{3}$ from both sides

∴ $-\frac{22}{3}$ = b

∴ y = $-\frac{2}{3}$ x - $\frac{22}{3}$

To draw the line substitute x by any two values and find their ys

∵ x = -2

∴ y = $-\frac{2}{3}$ (-2) - $\frac{22}{3}$  

∴ y = -6

∴ The line passing through point (-2 , -6)

∵ x = 1

∴ y = $-\frac{2}{3}$ (1) - $\frac{22}{3}$  

∴ y = -8

∴ The line passing through point (1 , -8)

∵ x = 4

∴ y = $-\frac{2}{3}$ (4) - $\frac{22}{3}$  

∴ y = -10

∴ The line passing through point (4 , -10)

Now we can make a table to draw the line

→  x  : -5  :  -2  :  1  :  4

→  y  : -4  :  -6  : -8 :  -10

Plot the points on the graph paper and draw the line

Look to the attached graph