Positive Slope

Positive slope refers to a line that is slant, and is inclined upwards when observed from left to right. The positive slope for a line can be calculated using the formulae m = (y₂ - y₁)/(x₂ - x₁) = Tanθ = f'(x) = dy/dx. The positive slope signifies that the two quantities represented along the two axes of the coordinate system increase or decrease at the same time. The line with a positive slope has the rise to run ratio, a positive value.

The line with a positive slope makes an acute angle with the positive x-axis. Let us learn more about the positive slope, the graph of the positive slope, how to calculate the slope, with the help of examples, FAQs.

A positive slope signifies that the two quantities represented along the x-axis and the y-axis are directly related.The increase or a decrease of one quantity makes a simultaneous increase or decrease in another quantity.. A line with a positive slope has m > 0 and the angle θ made by this line with the positive x-axis is an acute angle such that 0º < θ < 90º. The rise to run ratio of a line with a positive slope is also positive. Here the rise is the change in y value, which is represented as Δy, and the run is the change in x value, which is represented as Δx.

Positive Slope (m) = +rise/run = +Δy/Δx

A positive slope signifies that the two variables are directly related. Here as the x value increases the y value also increases. Alternatively, we can also observe that as the x value decreases the y value also decreases. Angle made by a line with a positive slope is in the anti-clockwise direction with respect to the positive x-axis or a line parallel to the x-axis is an acute angle. This acute angle is lesser than a right angle(90º-θ), and the slope of the line is a positive slope.

m = +Tanθ

The line with a positive slope is trending upwards from left to right. This can be observed in the graph below.

The concept of the positive slope indicates a direct relationship between the two quantities. The two quantities are represented graphically across the x-axis and the y-axis, and the line is plotted to represent the relationship between the two variables. As the value of the quantity represented along the x-axis increases, the value of the other quantity represented along the y-axis also increases. And this gives a line which is inclined upwards.

The direct relationship of increase of the x value, with the increase of the y value is represented by the positive slope of the line. Graphically the line with a positive slope is one that rises as it moves from left to right. The line with a positive slope makes an acute angle θ with the positive x-axis, in the anti-clockwise direction.

The positive slope of a line can be computed using three different methods. The positive slope of a line can be computed from any points on the line, the angle made by the line with the positive x-axis, or by taking a derivative of the function representing the curve . For the two points \((x_1, y_1)\) and \((x_2, y_2)\) on the line, the slope can be calculated using the formula m = \(\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\).

Also if θ is the angle made by the line with a positive x-axis in the anticlockwise direction, the slope of the line can be computed with the tangent of this angle θ. The angle made by a line with a positive slope is always an acute angle and can be taken as θ=90º - α. And we compute the slope using the formula m = Tan(90º - α) = +Tanα

For a given equation of a curve f(x), the slope of the curve is the slope of the tangent at the point on the curve and is calculated by taking the differentiation of the function. m = f'(x) = dy/dx.

Let us check a few examples of positive slopes.

• The price of a commodity and the quantity demanded to have a negative relationship. As the price increases, the quantity purchased is decreasing and the graph of such a line has a negative slope.
• The age of a young person and the height of the person if represented along the x-axis and y-axis, has an inclined line with a positive slope from left to right.
• The car moving up a steep road if observed is having a positive slope.
• The ramp along which people walk to move up an inclined plane is a simple example of a positive slope.

☛Related Topics

• Equation of Line
• Differentiation
• X and Y Coordinates
• Cartesian Plane

What Is A Positive Slope?

Positive slope refers to the slope of a line that is inclined upwards as we are moving from left to right. The angle made by a line with a positive slope is an acute angle with respect to the positive x-axis. A positive slope gives a direct proportional relationship between two variables. As the value of the x variable increase, the value of the y variable also increases.

How To Calculate Positive Slope From The Given Points?

The slope of a line connecting two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula m = \(\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\). The slope is the ratio of the difference between the y coordinate values, and the difference between the x coordinate values. The rise to run ratio of a line with a positive slope is also a positive value.

What Is the Difference Between Negative Slope And Positive Slope?

The negative slope and the positive slope is based on the sign of the slope value. The -ve value of the slope gives the negative slope and the +ve value of the slope gives the positive slope. The line with a negative slope is sloping downwards as it moves from left to right and the line with a positive slope is inclined as we are moving from left to right.

What Does Positive Slope Signify?

The positive slope signifies that the line is inclined upwards from left to right. Here the relationship between the two variables represented in the graph along the x-axis and the y-axis is directly proportional. The increase in one variable results in an increase in the other variable.

What Is The Relationship Between The Coordinates Of The Points For A Line With a Positive Slope?

For a line with a positive slope and passing through the two points \((x_1, y_1)\) and \((x_2, y_2)\), if the set of ordinates increase, the set of abscissa also increases. Also sometimes the ordinate value decreases, and also the abscissa value decreases.Here we can observe that as x₂ > x₁, we have y_2> y₁, OR as x₂ < x₁, we have y₂ < y₁.