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Graph (-5,-6) and has a slope of 2/3

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Answer:

To graph a line with a slope of 2/3 and passing through the point (-5,-6), we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is a point on the line.

Substituting m = 2/3 and (x1,y1) = (-5,-6), we get:

y - (-6) = 2/3(x - (-5))

Simplifying this equation, we get:

y + 6 = 2/3(x + 5)

Multiplying both sides by 3, we get:

3y + 18 = 2x + 10

Subtracting 2x and 18 from both sides, we get:

2x - 3y = -8

This is the standard form of the equation of a line. To graph this line, we can find its x- and y-intercepts by setting x=0 and y=0, respectively:

When x=0, we get:

2(0) - 3y = -8

Solving for y, we get:

y = 8/3

So the y-intercept is (0,8/3).

When y=0, we get:

2x - 3(0) = -8

Solving for x, we get:

x = -4

So the x-intercept is (-4,0).

Plotting these two points and connecting them with a straight line gives us the graph of the equation.

Explanation:

User Abdelrhman Adel
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