Write an equation of the line that passes through the given point and is perpendicular to...

Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. Write the answer in slope-intercept form. See Example.

EXAMPLE Write an equation of the line that passes through (6, -4) and is perpendicular to the line 3x + y = 2.

Strategy We will use the point-slope form, y — y1 = m(x — x1), to write the equation of the line.

WHY We know that the line passes through (6, -4). We can use the fact that the lines are perpendicular to determine the unknown slope of the desired line.

Solution

To find the slope of the given line, we must first solve for y to write the equation in slope-intercept form.

The slope of the given line is -3. The desired line is to have a graph that is perpendicular to y =- 3x + 2. Therefore, their slopes must be negative reciprocals. Its slope must be . We substitute 6 for x1, - 4 for y1, and for m in the point-slope form and simplify.

The equation is

 (0, 0), y = 4x − 7