Final answer:
To find the equation of a line that is perpendicular to the line 6x-y=4 and contains the point (-3,2), the slope of the given line is first determined. The slope of the perpendicular line is then found by taking the negative reciprocal of this slope. Using the point-slope form, the equation of the perpendicular line is determined by substituting the given point and the slope into the equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line 6x-y=4 and contains the point (-3,2), we first need to determine the slope of the given line. The equation of the given line is in the form y=mx+b, where m represents the slope. Rearranging the equation to slope-intercept form, we get y=6x-4. The slope of this line is 6.
Since the line we're looking for is perpendicular to the given line, its slope will be the negative reciprocal of 6. So the slope of the perpendicular line is -1/6.
Using the point-slope form y-y1=m(x-x1), where (x1,y1) represents the given point, we can substitute the values (-3,2) and -1/6 into the equation. Plugging these values in, we get y-2=-1/6(x+3). Simplifying the equation gives us y=(-1/6)x-1/2.