Question - Writing Linear Equations from a Table
mathslope and y-interceptlinear equations tablewriting linear equationscalculate slope and intercept
Solution:
To write the linear equation based on the provided table, we need to determine the slope and the y-intercept of the line.The slope (m) is the change in y divided by the change in x. Let's calculate it using the values from the table:m = (change in y) / (change in x)Looking at the y-values, each time x increases by 1, y decreases by 5 (for example, from -74 to -79, and from -79 to -84, etc.). So, our slope is -5.Now we need to determine the y-intercept (b), which is the value of y when x is 0. To find the y-intercept, we can use one of the points and the slope to write the equation. Let's take the first point (3, -74).y = mx + b-74 = -5(3) + bTo find b, we solve for it:-74 = -15 + bb = -74 + 15b = -59Now we have both our slope and our intercept. The linear equation in the form y = mx + b is:y = -5x - 59This is the equation that represents the rule shown in the table.
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