Graphing Linear Equations: Finding Intercepts

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In summary, to graph the equation y = 3x - 2, you can find the y-intercept by setting x to 0 and solving for y, which gives you the point (0,-2). Then, using the slope of 3, you can find the x-intercept by setting y to 0 and solving for x, which gives you the point (2/3,0). Plot these two points and draw a line connecting them to create the graph of the equation.
  • #1
Poweranimals
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How would I go about graphic this?

y = 3x - 2
 
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  • #2
As you alluded to in the subject of your post, a good way to graph the equation is to find the y intercept; and graph from there knowing the slope is 3. So set x to zero and determine the y intercept that way, then simply use the slope's ratio (3/1) and remember "rise over run".
 
  • #3
Or you can realize it is a linear equation and just take any two points, graph them, and connect them with a straight line.
 
  • #4
all you do is find the two intercepts and join them together...
remember that to find...
y-intercept, let x = 0 and
x-intercept, let y = 0...

so y-intercept = y = 3(0) - 2
y-int = -2
therefore ... (0,-2)

and x-intercept = 0 = 3x-2
3x = 2
x = (2/3)

(2/3,0)

so then you put a dot on those points and draw a line.
the line should be increasing since you know that the gradient is positive.
 

1. What is the purpose of graphing the y intercept?

The y intercept is the point where a line crosses the y-axis on a coordinate plane. Graphing the y intercept allows us to visualize the starting point of a linear equation and understand the relationship between the dependent variable (y) and the independent variable (x).

2. How do you find the y intercept on a graph?

To find the y intercept on a graph, look for the point where the line crosses the y-axis. This point will have an x-coordinate of 0 and the y-coordinate will be the value of the y intercept.

3. Can a line have more than one y intercept?

No, a line can only have one y intercept. This is because the y intercept is a specific point on the line where it crosses the y-axis. If a line had more than one y intercept, it would not be a straight line.

4. How does the y intercept affect the slope of a line?

The y intercept does not affect the slope of a line. The slope is determined by the rate of change between the y intercept and another point on the line. The y intercept simply represents the starting point of the line.

5. What does a y intercept of 0 mean?

A y intercept of 0 means that the line crosses the y-axis at the origin, where both the x and y coordinates are 0. This also indicates that the line passes through the point (0,0) on the coordinate plane.

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