Write an equation in slope-intercept form of the line satisfying the given condition.
Perpendiculst to y= 3/4x - 2 and passes through (-12,7)
Already answered below by bobpursley for "Lila"
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line first.
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
The given line equation is y = (3/4)x - 2. We can see that the slope of this line is 3/4.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the line perpendicular to this line will be -4/3.
Now we have the slope (-4/3) and the point that the line passes through (-12,7). We can substitute these values into the point-slope form of a line, which is y - y1 = m(x - x1).
Using (-12,7) as (x1,y1) and -4/3 as m, we get:
y - 7 = (-4/3)(x - (-12))
Expanding this equation further:
y - 7 = (-4/3)(x + 12)
To get the equation in slope-intercept form, we need to isolate y. So, let's distribute and simplify the equation:
y - 7 = (-4/3)x - 16
y = (-4/3)x - 16 + 7
y = (-4/3)x - 9
Therefore, the equation in slope-intercept form of the line that is perpendicular to y = (3/4)x - 2 and passes through the point (-12,7) is y = (-4/3)x - 9.