Final answer:
To determine a relationship between x- and y-values, use the linear equation form y = mx + b, where 'm' is the slope, and 'b' is the y-intercept. By identifying these components from an equation like y = 9 + 3x, you can graphically express the equation as a straight line on a graph.
Step-by-step explanation:
To determine a relationship between the x- and y-values and write an equation, you need to understand the format of a linear equation. A linear equation typically has the form y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept.
The slope, 'm', indicates the rate at which the y-values change relative to the x-values, also known as the 'rise over run'. The y-intercept, 'b', is the value of y when x is zero, or the point at which the line crosses the y-axis.
For example, if you are given the equation y = 9 + 3x, the slope 'm' is 3, indicating that for every one unit increase in x, y increases by 3 units. The y-intercept 'b' is 9, which is the point where the line crosses the y-axis. To express this equation graphically, you can plot values from the equation on a graph, connect the points, and you will have a straight line representing the equation.