How do you find the slope on a line graph?

Answer 1

Y-intercept Form From the formula y = mx + b

The y-coordinate of a point on the line equals the product of the slope of the line and the corresponding x-coordinate plus the y-intercept (the vertical line that runs through the point).

y - b = mx

m = y-b/x

Coordinate Points

The slope of a line can be seen visually and computed from the change between coordinates: the distance along the Y-axis divided by the distance along the X-axis, also known as the "rise over run." You can find the slope by finding whole-number coordinates for points that the line passes through. For a straight line, the slope of any segment is the slope of the line as a whole.

The formula is m= Δy/Δx

or m = (y1 - y2) / (x1 - x2)

- Find the Y-difference between the two points by subtracting the second from the first.

- Find the X-difference between the two points by subtracting the second from the first.

- Divide the Y-change by the X-change (one or both may be negative)

The slope will be the Y-change divided by the X-change. It is a positive slope for an upward slanting line, and a negative slope for a downward slanting line, as seen moving from left to right.

Rise over Run

The process is the same, except that you subtract the leftmost, lower X value from the larger X value to create a positive "run" number. Then you subtract the Y value of the leftmost point from the Y value of the rightmost point, giving you a "rise" that may be positive or negative.

Examples:

1) Finding the slope for a line that runs through the points (2,1) and (5,7). Start at the leftmost point and move right until you reach the other point. In this case, you should move across 3 spaces. So 3 is your "run." At the same time you are moving right, the Y value increases from 1 to 7. This is 6 and is your "rise."

Divide the Y-change by the X-change, rise over run, to get 6/3 or a slope of +2.

2) Finding the slope for a line that runs through the points (2,1) and (4, -3). Start at the leftmost point and move right until you reach the other point. In this case, you should move across 2 spaces. So 2 is your "run." At the same time you are moving right, the Y value decreases from 1 to -3. This is a drop of 4, or a "rise" (fall) of -4.

Divide the Y-change by the X-change, rise over run, to get -4/2 or a slope of -2.

As above, an upward slanting line has a positive slope, and a downward slanting line has a negative slope.