Learn how to write the equation of a straight line in slope-intercept form, y = mx + b, and how to find the slope and y-intercept. The slope is the steepness of the line and it can be positive, negative or zero.
Learn how to calculate the slope of a line using the formula y2-y1/x2-x1, where y2 and x2 are the coordinates of two points on the line. See how the slope can be positive, negative, zero or undefined depending on the direction of the line.
Slope is a value that describes the steepness and direction of a line. Learn how to calculate slope using the formula rise over run, and see examples of positive, negative, horizontal, vertical, parallel and perpendicular lines.
Thus, the slope formula is given as: Slope = m = (y 2 - y 1)/(x 2 - x 1) Slope Equation. As we discussed in the previous section, the slope formula can be used to determine the slope of any line. The equation that can be used in finding this slope can therefore written as, m = rise/run = tanθ = Δy/Δx = (y 2 - y 1)/(x 2 - x 1) where, m is the ...
For example, a line with equation y = (1/3)x + 4 has a slope of 1/3 (m=1/3) and a y-intercept at 4 (b=4). The formula for a slope of a line is the same formula for slope described above. As long as you know two points that a line passes through, you can use the formula for slope, m = (y2 - y1)/(x2 - x1), to find the slope of a line.
Positive Slope; Negative Slope; Zero Slope; Undefined Slope (also known as Infinite Slope) Note: The fourth on the list is not considered a type of slope because this is the case of a vertical line where the line is parallel to the y-axis, and it does not have a movement along the x-axis. In other words, a vertical line goes up and down ...
In this example, I’d like to show you that the numerical value of the slope is ALWAYS the same, regardless of which point you pick to be the “first” or “second”. As long as you maintain the correct order by subtracting the corresponding [latex]y[/latex] and [latex]x[/latex] coordinates, the slope should come out unchanged.
To find x or y intercepts, observe where the line on the graph cuts the x or y axis, respectively. The y-intercept is the point at which the line crosses the y-axis. The x-intercept is the point at which the line crosses the x-axis. Slope intercept form. y = mx + b, where m is the gradient or the slope and b is the y-intercept.
The slope of a line is the ratio between the change of \(y\) and the change of \(x\). Slope is sometimes expressed as rise over run. You can determining slope by visualizing walking up a flight of stairs, dividing the vertical change, which comes first, by the horizontal change, which come second. The slope, \(m,\) of a line is defined to be
The coefficient of x, when written in this form, is the slope. (Form means exact pattern.) So, if you saw the equation y = -2x + 5, you would instantly recognize that -2 is the slope. That means that the graph is going down from left to right. But, what if the equation was in Standard Form, like 2x – y = -5 (they’re actually the same equation).
In the example to the right, we are asked to determine the slope of the line that passes through the ordered pairs (-3,8) and (2,-11). We first identify the components of both ordered pairs by noticing which numbers are the x-values and which are the y-values. Then we substitute these numbers into the slope formula and calculate the slope.
The slope is which means that for every increase of 4 units in y, there is an increase of 3 units in x. Change in y is sometimes referred to as "rise" while change in x is referred to as "run." Note that even though we chose to use (4, 7) as x 2 and y 2, we could've also used it as x 1 and y 1 to achieve the same result:
The Slope Formula. We’ve seen that we can find the slope of a line on a graph by measuring the rise and the run. We can also find the slope of a line without its graph if we know the coordinates of any two points on that line.
The slope of this line = 3 3 = 1 So the slope is equal to 1. In other words for every 3 steps right, the line goes up 3 steps. Since both are the same, the slope is 1.
Negative slope: Y-values are decreasing/decaying compared to the x-values. 0-slope: There is no change in y-values compared to the x-values. The larger the slope, the steeper the line, or in other words, the greater the rate of change. The smaller the slope, the slower the growth or decay and slower the rate of change.
What Does the Slope of a Line Mean? You can't learn about linear equations without learning about slope. The slope of a line is the steepness of the line. There are many ways to think about slope. Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. Check out this tutorial to learn about slope!
The formula is \(m = \frac{y_2-y_1}{x_2-x_1}\), where \(m\) is the slope, \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line. The slope formula is typically covered in a high school algebra or geometry class. A fun fact about the slope formula is that it can be used to determine whether two lines are parallel or perpendicular. If the ...
Slope is rise over run, change of y over x, rate of change. Learn everything Algebra 1 students needs to know about slope and math.
