Question

perpendicular to the line 2x-5=-11; Vrite the point-slope form of the equation wi slope =(1)/(2);x-intercept =3 slope =-3; passes through (4,-7)

Answer 1

The point-slope form of the equation of the line that is perpendicular to 2x - 5 = -11, with a slope of 1/2 and passes through the point (4, -7), is y = (-1/2)x - 5.

Step-by-step explanation:

The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)

Given that the line is perpendicular to 2x - 5 = -11, we can rewrite this equation in slope-intercept form as y = 2x + 6. Since the slopes of perpendicular lines are negative reciprocals of each other, the slope of the line we are looking for is -1/2.

Now, using the point-slope form, we can substitute the given point (4, -7) and the slope (-1/2) into the equation:

y - (-7) = (-1/2)(x - 4)

y + 7 = (-1/2)x + 2

y = (-1/2)x - 5