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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.
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Is the first derivative of a function is a constant then its graph is?
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
What is the steepness on a line graph called?
The steepness of a line graph is called the "gradient" ------------------------------- or slope.
How do you graph y equals 2x-3?
5
How do you graph g of x equals 5x?
It is a straight line through the origin with slope of 5. So start at (0,0) and go up 5 and over 1 to find the next point. Join those two points with a line and you can see the graph.
When there is no change in value from one data point to the next in a line graph what type of slope does the line that connects them have?
The slope is zero. Slope is rise over run, the rise is zero, so zero divided by anything is zero.
Find the slope of a tangent line to the graph?
Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.
Find the constant of variation and the slope of the given line from the graph of y equals 2.5x?
find the constant of variation and the slope of the given line from the graph of y=2.5x
Is the steepness of a line on a motion graph is called a slope?
"Slope" is the steepness of the line on any graph.
Find the slope of a parellel to the graph of y equals 4x plus 2?
The graph of [ y = 4x + 2 ] is a straight line with a slope of 4.Any line with a slope of 4 is parallel to that one, and any line parallel to that one has a slope of 4.
What is the slope of a graph line?
it is impossible to tell the slope of a line graph without proper points to evaluate from.
How do you tell whether a graph shows a constant or variable rate of change?
The slope of each point on the line on the graph is the rate of change at that point. If the graph is a straight line, then its slope is constant. If the graph is a curved line, then its slope changes.
The graph of which line has a slope of 2?
The graph of the equationy = 2x + any numberis a straight line with a slope of 2.
The slant of a line on a graph is called?
the slope.
What is the slope of a line on distance time graph?
acceleration
Is the first derivative of a function is a constant then its graph is?
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
What happends to the graph of a line when the slope is negative?
A straight line graph with negative slope slants downward from left to right.
How do you determine the speed of an object by looking at a graph?
To determine the speed of an object from a graph, you can calculate the average speed by finding the slope of the line connecting two points on the graph. The steeper the slope, the higher the speed. Alternatively, you can also find the instantaneous speed by looking at the slope of the tangent line at a specific point on the graph.
