Write an equation in slope-intercept form of the line satisfying the given conditions.
Through (6,7), perpendicular to negative 2 x minus 3 y equals negative 24
To write an equation in slope-intercept form, we need to determine the slope and the y-intercept.
Given the equation of the line perpendicular to -2x - 3y = -24, we can rewrite it in slope-intercept form by isolating y:
-2x - 3y = -24
-3y = 2x + 24
y = (-2/3)x - 8
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the line we are looking for will be the negative reciprocal of (-2/3), which is 3/2.
Now we have the slope (3/2) and the point (6, 7).
Using the point-slope form of a linear equation, we can write the equation as:
y - 7 = (3/2)(x - 6)
To convert it into slope-intercept form, we need to simplify and isolate y:
y - 7 = (3/2)x - 9
y = (3/2)x - 9 + 7
y = (3/2)x - 2
Therefore, the equation of the line satisfying the given conditions is y = (3/2)x - 2.