what is Graphing Linear Equation using Slope intercept form

Question

Simply answer this question. I am confused about these things. Please help! THANK YOU SO MUCH 😀

Answer 1

Graphing a linear equation using slope-intercept form means plotting a straight line on a coordinate plane where the equation is written as:

y= mx+b

Here:

1. m is the slope of the line,
2. b is the y-intercept (the point where the line crosses the y-axis).

Steps to graph a linear equation using slope-intercept form:

1. Identify the y-intercept b:
2. This is the point (0,b) on the graph.
3. Start by plotting this point on the y-axis.
4. Use the slope mm:
5. Slope m is the rise over run:
6. m=change in y / change in x =Δy/Δx
7. From the y-intercept point, move up or down by the rise (Δy) and right or left by the run (Δx) to plot another point.
8. If mm is positive, go up; if negative, go down.
9. Always move to the right for the run (positive x-direction).
10. Draw the line:
11. Connect the two points with a straight line extending in both directions.

Answer 2

if a linear equation is solved for y,

then the coefficient of the x term = the slope and the constant term = y intercept

for example,

4x +2y = 6, subtract 4x from both sides

2y =-4x+6 divide both sides by 2

y = -2x +3, slope =-2 and y intercept = +3 or the point (0,3)

-2 slope means downward sloping, going left to right, down 2 for every 1 unit to the right, so

another point on the line is (0+1, 3-2) = (1,1). Plot those two points, connect them with a straight line,

that's the graph of the linear equation

a possibly easier way to graph it might be to also solve for the x intercept, where the line intersects the x axis, set y=0 and solve for x

when y=0 then x=6/4 = 3/2, the point (3/2, 0) = (1.5, 0)

plot those two points (0,3) and (3/2, 0) connect them with a straight line, extend the line beyond the 2 points and put arrows at their ends indicating the line goes forever, and ever. Amen.

Answer 3

When a linear equation is written in slope-intercept form, y = mx + b, it is easy to graph.

1) Plot the y-intercept which is (0, b). (The y-intercept is an ordered pair.)

2) Then use the slope, m, to plot other points. The slope can be written as a fraction, if it it isn't already, and use rise over run to plot other points.

Example:

y = 2/3 x - 5

1) The y-intercept is (0, - 5). That is the first point you would plot.

2) The slope, m, is 2/3. From the y-intercept, go up 2 units and to the right 3 units and plot that point.

Answer 4

Hi Amy!

First, let's clear up the terminology. A "linear equation" in this context means an equation involving two variables, usually x and y, in which both sides only have constants and "linear terms," which, in this case, would be a constant multiple of x or y. For example the equation

-2x+4y=3

is considered linear, since -2x is the product of a constant, -2, with x, and 4y is the product of a constant, 4, with y, and since 3 is a constant. This means all terms on either side of the equation are linear or constant terms, making the equation a linear equation. Other examples of linear equations are

x=4

y=-x-1

4y=x+1

Now, an equation is in slope-intercept form if on one side of the equation is solely the variable y and on the other side the sum of a linear term in x (e.g. 5x) and a constant term. Some examples are

y=2x-1

y=0.5x+6

y=-x+8

The coefficient of the linear term (the constant being multiplied with the variable, e.g. the 5 in 5x) in a linear equation in slope-intercept form is called the slope. So, in y=2x-1, the slope is 2. The y-intercept is the constant term, so in y=2x-1, the y-intercept is -1. In the equation y=2x-1, when you plug the numbers 0, 1, 2, 3, 4 in for x, you obtain -1, 1, 3, 5 for y, respectively. On a graph, these are the points (0, -1), (1, 1), (2, 3), and (3, 5). I encourage you to draw it on a piece of paper. Visually, these points form a line. Since when x increases by 1, y increases by 2, on the graph one can draw the "rise" (how much y increases, 2) and the "run" (how much x increases, 1) so that the slope is the "rise over the run," which is 2/1=2. When you draw the line that goes through these points, that's what it means to graph the linear equation. The y-intercept is the y-value at which the line intersects the y-axis. The point (0, -1) lies on the y-axis and on the line y=2x-1, visually allowing us to see that the y-intercept is -1.

Slope-intercept form makes it easy to graph linear equations. To graph a line, generally you only need two points. The linear equation being in slope-intercept form immediately gives us the y-intercept, so, e.g., if we're graphing y=-2x+3, since 3 is the y-intercept, we can immediately plot (0, 3). To find a second point, we can use the slope. In the case of y=-2x+3, since the slope is -2, when we go to the right on the line by 1 (increasing x by 1), we should be going down by 2 (decreasing y by 2, i.e. increasing y by -2). So, starting from (0,3) we know (0+1, 3-2), which is (1, 1), is on our line. This gives us two points to draw the line through.

Not all linear equations are in slope intercept form. For example, 6=6x+3y isn't in slope-intercept form. If we want to put it in slope-intercept form to make it easier to graph, we need to rearrange the equation so the y is on one side and that the other side only has numbers and the variable x. We can rearrange 6=6x+3y as follows:

6 = 6x+3y

6-6x = 6x+3y-6x (subtracting 6x from both sides)

6-6x = 3y (simplifying right-hand side)

2-2x = y (dividing both sides by 3)

y = -2x+2 (using symmetry of equality)

Now, we can graph y=-2x+2 using slope-intercept form using the same process described above!