4. What is the equation in slope-intercept form of the line that passes through the point $(5,4)$, and is parallel to the line represented by $y=2 x+12$ ?
Answer
Final Answer: The equation of the line in slope-intercept form that passes through the point \((5,4)\), and is parallel to the line represented by \(y=2 x+12\) is \(\boxed{y = 2x - 6}\).
Step 1 ：The slope-intercept form of a line is given by \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.
Step 2 ：The slope of a line parallel to another line is the same as the slope of the original line. Therefore, the slope of the line we are looking for is 2, the same as the slope of the line \(y=2x+12\).
Step 3 ：We can find the y-intercept by substituting the coordinates of the given point into the equation and solving for \(c\). So, we have \(4 = 2*5 + c\).
Step 4 ：Solving this equation for \(c\), we get \(c = -6\).
Step 5 ：Final Answer: The equation of the line in slope-intercept form that passes through the point \((5,4)\), and is parallel to the line represented by \(y=2 x+12\) is \(\boxed{y = 2x - 6}\).
