The slope of a line is a quantity that is used to describe the steepness and the direction of the line. When the equation of a line is written in the slope-intercept form, it is easy to determine the slope of the line from the equation. The structure of the slope-intercept form of linear equations is y = mx + c, where m is the slope of the line and c is the line's y-intercept, which is the value of the y-coordinate of the point where the line intersects the y-axis.

To graph a line that has a fractional slope, we can use the following steps:

1) Write the equation of the line in slope-intercept form, y =mx + c.

2) Determine the coordinates of the y-intercept of the line, i.e., (0, c). The x-coordinate of the y-intercept is always 0.

3) If the slope has an integral value, then, starting from the y-intercept, we move a number of steps in the y and the x directions as dictated by the slope (m) of the line. Note that the formula for calculating the slope of a line is slope = (change in y-coordinates)/(change in x-coordinates). Thus, if the slope is 2, starting from the y-intercept, we move 2 steps along the positive y-direction and 1 step along the positive x-direction.

If the slope is a fraction of the form `\frac{s}{t}` , then, starting from the y-intercept, we move s steps in the y-direction and t steps in the x-direction (remember to move either in the positive or negative x and y directions per the sign of the slope) to the new point (x, y).

4) Use the points (0, c) and(x, y) to graph the line.

Example: Plot `y = \frac{-1}{2} x + 1` .

In this case, the slope is a fraction, `\frac{-1}{2}` . Thus, starting from the y-intercept, we should move 1 step in the negative y-direction and 2 steps in the positive x-direction.

The y-intercept here is (0, c), where c is 1 from y = `\frac{-1}{2}x + 1` . Thus, we start from the point (0, 1) and move 1 step in the negative y-direction to the point 0; we also move 2 steps in the positive x-direction to the point 2. The coordinates of the new point are (2, 0).

On the Cartesian plane, we join the points (2, 0) and (0, 1) with a straight line as shown in the attachment.

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