Find the equation of the line containing the point (-3, 2) and perpendicular to the line .

Question

Find the equation of the line containing the point (-3, 2) and perpendicular to the line  .

Quizplus · Accepted Answer

To find the equation of a line perpendicular to another line, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other. First, we need to find the slope of the given line. The line 11eb69da_9ee2_9b3c_af94_3bc67c1b08d6_TB8311_11 is in the form y = mx + b, where m is the slope. So rearranging this equation to get it in slope-intercept form, we have y = (5/2)x + 5. Therefore, the slope of this line is m = 5/2.

Since we want to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of 5/2. The negative reciprocal is simply flipping the fraction and changing the sign, so the negative reciprocal of 5/2 is -2/5.

Now we have the slope of the line we want, and we also have a point that the line passes through (-3, 2). We can use the point-slope form of a linear equation to find the equation of this line. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is the point that the line passes through. Substituting in the values we have:

y - 2 = (-2/5)(x - (-3))

Simplifying:

y - 2 = (-2/5)x - (6/5)

y = (-2/5)x + (4/5)

This is the equation of the line we want, in slope-intercept form. So the answer is choice B.

Find the Equation of the Line Containing the Point (-3