Problem 97
Question
Explain how to use the general form of a line's equation to find the line's slope and \(y\) -intercept.
Step-by-Step Solution
Verified Answer
Identify 'm' as the coefficient of 'x' and 'b' as the constant term in the equation \(y = mx + b\). 'm' is the slope and 'b' is the \(y\)-intercept.
1Step 1: Identifying 'm' and 'b' from the equation
Let's begin by reviewing the equation. Purposefully look for the values that correspond to 'm' and 'b'. 'm' is the coefficient in front of 'x', while 'b' is the constant term.
2Step 2: Confirming the slope
Verify the 'm' value represents the slope. Remember that the slope measures the steepness of the line. A slope can be positive, negative, or zero, and respectively the line slope upwards, downwards, or is horizontal.
3Step 3: Verifying the \(y\)-intercept
Confirm the 'b' value is the \(y\)-intercept. This is the 'y' value where the line crosses, or intercepts, the \(y\)-axis. If the line does not cross the \(y\)-axis, then there is no \(y\)-intercept.
Other exercises in this chapter
Problem 96
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