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What is the gradient of a line graph?
The gradient of a straight line describes the slope or steepness of the line. To determine the gradient of a line: choose any two points on the line. draw a right-angled triangle from one to the other, using the line as the hypotenuse.
How do you describe the gradient of a line?
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Sometimes the ratio is expressed as a quotient (“rise over run”), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative “rise”.
What is a gradient graph?
Gradient is another word for “slope”. The higher the gradient of a graph at a point, the steeper the line is at that point. A negative gradient means that the line slopes downwards.
What does the gradient of the graph represent?
The gradient of a line or, more generally, a curve plotted on an xy-axes tells us how the change in the y-value of the curve depends on the x-value. Here x denotes the time, and y the distance. The gradient of a graph of distance versus time gives us the velocity.
How do you plot a line on a gradient graph?
The gradient of the line = (change in y-coordinate)/(change in x-coordinate) . We can, of course, use this to find the equation of the line. Since the line crosses the y-axis when y = 3, the equation of this graph is y = ½x + 3 . To find the gradient of a curve, you must draw an accurate sketch of the curve.
How do you find the equation of a line with a gradient?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
How to calculate the gradient of a line?
If two lines are perpendicular, then their gradients will multiply together to give -1. Find the equation of a line perpendicular to y = 3 – 5x. This line has gradient -5. A perpendicular line will have to have a gradient of 1/5, because then (-5) × (1/5) = -1. Any line with gradient 1/5 will be perpendicular to our line, for example, y = (1/5)x.
What does it mean when a graph has a gradient?
Gradient is another word for “slope”. The higher the gradient of a graph at a point, the steeper the line is at that point. A negative gradient means that the line slopes downwards. The video below is a tutorial on Gradients. Finding the gradient of a straight-line graph. It is often useful or necessary to find out what the gradient of a graph is.
Is the gradient of a straight line positive or negative?
That line goes down as you move along, so it has a negative Gradient. A line that goes straight across (Horizontal) has a Gradient of zero. so a “straight up and down” (vertical) line’s Gradient is “undefined”. Sometimes the horizontal change is called “run”, and the vertical change is called “rise” or “fall”:
When do two lines have the same gradent?
Two lines are parallel if they have the same gradent. The lines y = 2x + 1 and y = 2x + 3 are parallel, because both have a gradient of 2. Two lines are perpendicular if one is at right angles to another- in other words, if the two lines cross and the angle between the lines is 90 degrees.