Question

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

Answer 1

Considering the definition of a line, the equation of the line that passes through the point (-5, -4) and has a slope of -2/3 is y= -2/3x -22/3 and the graph is attached.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

• x and y are coordinates of a point.
• m is the slope.
• b is the ordinate to the origin.

Line in this case

In this case, you know:

• The line has a slope of -2/3.
• The line passes through the point (-5, -4).

Substituting the value of the slope and the value of the point in the expression of a linear equation, the value of the ordinate to the origin can be obtained:

-4= -2/3×(-5) + b

-4= 10/3+ b

-4 - 10/3= b

-22/3= b

Finally, the equation of the line that passes through the point (-5, -4) and has a slope of -2/3 is y= -2/3x -22/3 and the graph is attached.

Answer 2

The figure is attached down

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
`-(2)/(3)`

∴ y =
`-(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 =
`-(2)/(3)` (-5) + b

∴ -4 =
`(10)/(3)` + b

- Subtract
`(10)/(3)` from both sides

∴
`-(22)/(3)` = b

∴ y =
`-(2)/(3)` x -
`(22)/(3)`

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

∵ x = -2

∴ y =
`-(2)/(3)` (-2) -
`(22)/(3)`

∴ y = -6

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

∵ x = 1

∴ y =
`-(2)/(3)` (1) -
`(22)/(3)`

∴ y = -8

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

∵ x = 4

∴ y =
`-(2)/(3)` (4) -
`(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