graph the equation.\n9. y = x + 5\n10. y = x - 7\n11. y = -4x + 1\n12. y = 2x\n13. y = \\frac{1}{3}x +…

: To graph the linear - equations (y = mx + b) (where (m) is the slope and (b) is the y - intercept), we can follow these steps for each equation:

For (y=x + 5):

1. The y - intercept (b = 5), so the line crosses the y - axis at the point ((0,5)).
2. The slope (m = 1=\frac{1}{1}), so from the point ((0,5)), we move 1 unit up and 1 unit to the right to get another point ((1,6)). Then we draw a straight line through these two points.

For (y=x - 7):

1. The y - intercept (b=-7), so the line crosses the y - axis at the point ((0, - 7)).
2. The slope (m = 1=\frac{1}{1}), so from the point ((0,-7)), we move 1 unit up and 1 unit to the right to get another point ((1,-6)). Then we draw a straight line through these two points.

For (y=-4x + 1):

1. The y - intercept (b = 1), so the line crosses the y - axis at the point ((0,1)).
2. The slope (m=-4=\frac{-4}{1}), so from the point ((0,1)), we move 4 units down and 1 unit to the right to get another point ((1,-3)). Then we draw a straight line through these two points.

For (y = 2x):

1. The y - intercept (b = 0), so the line crosses the y - axis at the point ((0,0)).
2. The slope (m = 2=\frac{2}{1}), so from the point ((0,0)), we move 2 units up and 1 unit to the right to get another point ((1,2)). Then we draw a straight line through these two points.

For (y=\frac{1}{3}x+2):

1. The y - intercept (b = 2), so the line crosses the y - axis at the point ((0,2)).
2. The slope (m=\frac{1}{3}), so from the point ((0,2)), we move 1 unit up and 3 units to the right to get another point ((3,3)). Then we draw a straight line through these two points.

For (y=-\frac{1}{4}x + 3):

1. The y - intercept (b = 3), so the line crosses the y - axis at the point ((0,3)).
2. The slope (m=-\frac{1}{4}), so from the point ((0,3)), we move 1 unit down and 4 units to the right to get another point ((4,2)). Then we draw a straight line through these two points.

For (y=\frac{2}{3}x-1):

1. The y - intercept (b=-1), so the line crosses the y - axis at the point ((0,-1)).
2. The slope (m=\frac{2}{3}), so from the point ((0,-1)), we move 2 units up and 3 units to the right to get another point ((3,1)). Then we draw a straight line through these two points.

For (y=-\frac{3}{4}x-3):

1. The y - intercept (b=-3), so the line crosses the y - axis at the point ((0,-3)).
2. The slope (m=-\frac{3}{4}), so from the point ((0,-3)), we move 3 units down and 4 units to the right to get another point ((4,-6)). Then we draw a straight line through these two points.

Explanation:

Step1: Identify y - intercept

Find the value of (y) when (x = 0). This gives the point ((0,b)) where the line crosses the y - axis.

Step2: Identify slope

The slope (m) in the equation (y=mx + b) gives the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. Use the slope to find a second point from the y - intercept.

Step3: Draw the line

Draw a straight line passing through the y - intercept and the second point found using the slope.