Question

The equation of line WX is 2x + y = -5. What is the equation of a line perpendicular to line WX in slope-intercept form that contains point (-1, -2)?

Answer 1

Answer:

The third choice is the one you want

Step-by-step explanation:

If we are to write the equation of a line perpendicular to WX, we first must determine what the slope of the WX is, because the line perpendicular to WX has a slope that is the flip of the slope of WX with the opposite sign.  Solving for y takes care of finding the slope of WX:

2x + y = -5 so

y = -2x - 5

The slope is -2.  That means that the reciprocal slope is 1/2.  Using that slope along with the coordinates x = -1 and y = -2, we first write the line using point-slope form and then solve it for y.  Start by filling in the m, the x value and the y value:

$y - (-2) = \frac{1}{2}(x-(-1))$

Getting rid of the double negatives gives us:

$y+2=\frac{1}{2}(x+1)$

Distributing then gives us:

$y+2=\frac{1}{2}x+\frac{1}{2}$

And finally solving for y (I am going to express the 2 on the left as 4/2 when I move it by subtraction in order to add those fractions):

$y=\frac{1}{2}x+\frac{1}{2}-\frac{4}{2}$

And the final equation in slope-intercept form is:

$y=\frac{1}{2}x-\frac{3}{2}$

Answer 2

Remember that when a line is perpendicular to a line with slope m, then slope of that perpendicular line is -1/m.

The equation of line which is perpendicular to WX in slope-intercept form, passing through point (-1,-2) is given by:

$y = \dfrac{1}{2}x -\dfrac{3}{2}$

Given that:

• Equation of line WX is: 2x + y = -5

• The other line is perpendicular to WX and passes through (-1,-2)

To find:

• Equation of that other line.

Formation of equation:

Slopes of two lines perpendicular to each other are negative reciprocal of each other.

The equation of WX, when written in slope intercept form will be:

$y = -2x - 5$

The slope of WX is -2 and intercept is at y = -5

Let that other line is represented by L.

Then the slope of L would be negative reciprocal of 2 which is $\dfrac{1}{2}$

Thus equation of L would be:

$\\ y = \dfrac{1}{2}x + c$ where c represents y intercept.

Since the line L passes through the point (-1,-2), thus that point must satisfy the equation of L, or:

$-2 = \dfrac{1}{2}\times -1 + c\\\\-2+\dfrac{1}{2} = c\\\\c = -\dfrac{3}{2}$

Thus, slope intercept form of line L is given by:

$y = \dfrac{1}{2}x -\dfrac{3}{2}$

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