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: