Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-4,7);y=1/4x-2
To find the equation of a line that is perpendicular to another line, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
The given equation is in slope-intercept form: y = (1/4)x - 2. The slope of this line is 1/4.
The slope of the line perpendicular to this line would be the negative reciprocal of 1/4. In other words, it would be -4/1 or -4.
So, the equation of the line passing through the point (-4, 7) with a slope of -4 is given by the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. Plugging in the values:
7 = (-4)(-4) + b
7 = 16 + b
To isolate b, we subtract 16 from both sides:
7 - 16 = b
-9 = b
Thus, the equation of the line that passes through the point (-4, 7) and is perpendicular to the given line y = (1/4)x - 2 is:
y = -4x - 9