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.