Graph the line that passes through the points (-6, -4) and (-5, -4) and
determine the equation of the line.

Answer:

Step-by-step explanation:

The equation of the line passing through the points [tex](x_{1},y_{1} ) and (x_{2} ,y_{2} )[/tex] is

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )[/tex]

plug the two points [tex](x_{1},y_{1} )=(-6,-4) and (x_{2} ,y_{2} )=(-5,-4)[/tex] into the equation.

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)[/tex]

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)\\y+4=0\\y=-4[/tex]

The equation of line that runs through the points (-6, -4) and (-5, -4) is y = -4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line that passes through the points (-6, -4) and (-5, -4).

First, we find the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -4 - (-4) )/( -5 - (-6) )

Slope m = ( -4 + 4 )/( -5 + 6 )

Slope m = ( 0 )/( 1 )

Slope m = 0

Next, find the y-intercept b.

y = mx + b

Plug in slope m = = and point 1( -6, -4 )

-4 = 0(-6) + b

Solve for b

-4 =  b

b = -4

Now, plug slope m = 0 and y-intercept b = -4 into the slope intercept form to determine the equation of the line.

y = mx + b

y = 0(x) + -4

y = -4

Therefore, the equation of line is y = -4.

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