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How do you change equations into the y = mx + b form? Are there specific steps or a worksheet to follow?

User Taveras
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Final answer:

To change equations into the y = mx + b form, isolate y by moving terms, combining like terms, and dividing by any coefficient of y. Then arrange the terms so that y = mx + b, where m is the slope and b is the y-intercept. Expressing the equation graphically involves plotting (x, y) points and drawing a line through them.

Step-by-step explanation:

To change equations into the y = mx + b form, also referred to as the slope-intercept form, you follow several steps. The goal is to solve the equation for y so that you have y on one side of the equation by itself, and everything else on the other side. Here’s a general guide to doing this:

  • If the equation has terms on both sides of the equals sign, start by moving all the terms involving y to one side and the other terms to the opposite side. You can do this through addition or subtraction.
  • Once you have all the y-terms on one side, combine like terms if necessary.
  • If y is being multiplied by a coefficient other than 1, you need to isolate y by dividing the entire equation by that coefficient.
  • Once y is isolated, arrange the terms so that you have y on one side and terms of the form mx + b on the other, where m is the slope and b is the y-intercept.

For example, with the equation y = 9 + 3x, it is already in the y = mx + b form, where 3 is the slope (m), and 9 is the y-intercept (b).

To express equations graphically, you can construct a table of values by plugging in different values for x and calculating the corresponding y values. These pairs of (x, y) points can then be plotted on a graph, and a straight line can be drawn through them to visually represent the linear relationship defined by the equation.

User Peter Lamberg
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