Final answer:
The question asked for a linear equation based on the values in a table. We've found the slope to be 4 and the y-intercept to be -2, leading to the linear equation y = 4x - 2.
Step-by-step explanation:
To write a linear equation that fits the values in the given table, we need to find the slope and the y-intercept. The slope is calculated by the change in y over the change in x (rise over run). Looking at the provided table, we can choose two points to calculate the slope. For example, using the points (1, 2) and (3, 10), the slope would be (10 - 2) / (3 - 1) = 8 / 2 = 4. The slope is therefore 4.
To find the y-intercept, we can look for the value of y when x is 0. However, since we don't have the point where x is 0 in the table, we can use the slope we've just found to back-calculate from a known point. Using the point (1, 2), the equation format is y = mx + b where m is the slope and b is the y-intercept. Now we plug in the values (1, 2) into the equation 2 = 4*1 + b to find that b = 2 - 4 = -2. So, the y-intercept is -2.
The linear equation that fits the table data is y = 4x - 2.