Question 9 of 11, Step 1 of 1 Correct Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer. Point $(-5,11) ;$ Slope $=-2$ Answer
Solution
Step 1 ：The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We are given the slope \(m = -2\) and a point on the line \((-5,11)\). We can substitute these values into the equation to solve for \(b\).
Step 2 ：Substituting the given values into the equation, we get \(11 = -2(-5) + b\). Solving for \(b\), we find that \(b = 1\).
Step 3 ：Now that we have the slope and the y-intercept, we can substitute these values into the slope-intercept form of the equation to get the equation of the line.
Step 4 ：Substituting \(m = -2\) and \(b = 1\) into the equation, we get \(y = -2x + 1\).
Step 5 ：Final Answer: The equation of the line in slope-intercept form that passes through the point \((-5,11)\) with the slope \(-2\) is \(\boxed{y = -2x + 1}\).
