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y=mx+b means that m is the slope, x is the variable, and b is the y intercept.
[ADDED] The gradient m is given by the difference formula [ y2 - y1) / (x2 - x1) ] where the 1 and 2 signify separate ordinates and the y-values are those from their corresponding x-values.
NB: they are not powers or factors here, but the text editor's limits makes typing algebra difficult.
In words, it is the change in the y-value given by a chosen change in the x-value.
So if the equation is y = 3x, lets take the values of x as 1 and 4. Therefore, the slope = [ (12-3) / (4-1) ]
= 9/3 = 3.
Important: always take the 1 and 2 co-ordinates in that rising-x order, not necessarily smaller-from-larger in y, because if the graph slopes down to the right the y-difference will be a negative number so the gradient is negative, and that is its correct description.
AS AN ASIDE because we need not complicate things by invoking calculus for simple linear graphs, that difference-over-difference formula in calculus notation is shown by the operator, dy/dx; and the process is called "differentiation". Worth recalling when you proceed to studying Calculus, which analyses non-linear equations!
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How do you find the equation of a graph?
You find the equation of a graph by finding an equation with a graph.
How do you find the y intercept of a linear relationship from an equation?
plug in a 0 for the "x" value of the equation, and solve it :D
How do you graph the linear equation xy 4?
There are many ways to graph linear equations. One way that will always work it to pick some points, 3 is plenty. Pick and x value, plug it in and then find the y value. You will obtain a set or ordered pairs. Graph these and connect the dots. Voila------------- a line!
How do you graph linear functions?
A linear function is called "linear" because it represents a straight line. To graph a linear function, find two points that satisify that function, plot them, and then draw a straight line between them.
How do you graph the equation y equals -x-3?
Here is a simple way to graph a linear equation. A linear equation is one that has a y term (a number times y), an x term and a constant (but no squares or cubes or square roots etc.): Let x = 0 and use the equation to find y. This gives you one point on the graph: (0, -3) Let y = 0 and use the equation to find x. This gives you another point on the graph (3, 0) Plot these two points, join them with a line and extend in both directions. However, this method gives only one point if the equation is of the form y = ax where a is some non-zero constant; and that point is (0,0) In that case, use (1,a) as the second point.
How do you find the equation of a graph?
You find the equation of a graph by finding an equation with a graph.
3s equals 2t is this a linear equation or nonlinear?
3s=2t can also be written as 3y=2x or 3x=2y. Either way, it is linear. To find out if it is linear, simply graph it. If you can draw a completely vertical line through any point of the graph without intersecting more than one point of the graph, then it is linear. This equation (3s=2t), it is linear.
How do you find an equation from a graph?
In general, it is very difficult. Even if a graph looks like a straight line over the domain there is no guarantee that the underlying equation makes the equation non-linear as you move away from the visible domain. A typical example, from school physics, concerns Hooke's law. The extension of a length of wire under different strains follows a linear relationship. Until the strain reaches a critical level and then the relationship goes all haywire. Looking at the graph below that critical level, the equation would be a straightforward linear one. But that is true only as far as it goes.
How do you know if numbers show linear relationship?
A linear equation looks like any other equation. It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as straight lines.
How do you find the y intercept of a linear relationship from an equation?
plug in a 0 for the "x" value of the equation, and solve it :D
How can you find the y intercept of the graph of a linear equation?
At a y-intercept, the graph touches the y-axis, meaning the value of x is 0. So, in any linear equation, simply set x equal to 0 and solve for y. In the slope-intercept form of a linear equation (y = mx + b), the y-intercept value is represented by the variable b.
How do you find the y-intercept of a linear relationship from a graph?
To find the y-intercept from a graph - look at where the graph of the line intersects the y-axis. The point at where the graph of the line crosses the y-axis will be the y-intercept with the coordinates of (0,y) The point at which the line cuts the y – axis is called as y – intercept.You can locate the point by seeing the graph.Note:If you are given a linear equation say ax + by + c = 0Now if we plug x = 0 in the given equation we will get the y – intercept.y = -c/bIf the given equation is of the form y = mx + bb is the y – intercept of the line. Source: www.icoachmath.com
How do you find the x intercept on a linear equation?
At the x-intercept on the graph of the equation, y=0. Take the equation, set 'y' equal to zero, and solve the equation for 'x'. The number you get is the x-intercept.
How do you find an equation of a linear function?
how do we find linear feet or inche
What are the steps to solve a Linear Equation?
1.Put into y=mx=b 2.graph 3. find ordered pair where the lines intersect
How do you find the y-intercept of a linear relationship from an equation?
The y-intercept of a linear equation is the point on the y-axis at which the line cuts.It could be found by plugging x = 0 in the given linear equation.For example,Consider 3x + 2y = 6. To find the y-intercept just plug x = 0 in the equation.3(0) + 2y = 62y = 6y = 3(0, 3) is the y-intercept of the linear equation 2x + 3y = 6.Note:In the same way we can find the x-intercept by plugging y = 0 in the given linear equation.
How do you graph the linear equation xy 4?
There are many ways to graph linear equations. One way that will always work it to pick some points, 3 is plenty. Pick and x value, plug it in and then find the y value. You will obtain a set or ordered pairs. Graph these and connect the dots. Voila------------- a line!
