Question

write the equation of the line that passes through the point (2,-3) and is perpendicular to the line y=-2x+3. And how do you find it?

Answer 1

The equation for the line perpendicular to y = -2x + 3 that passes through the point (2, -3) is y = ½x - 4. Find this by using the negative reciprocal of the original line's slope and the point-slope form of a line equation.

Step-by-step explanation:

To write the equation of the line that is perpendicular to another line, you need to find the slope that is the negative reciprocal of the original line's slope. The given line is y = -2x + 3, which has a slope of -2. The perpendicular line will thus have a slope of ½ (since the negative reciprocal of -2 is ½).

Next, we use the point-slope form of the equation for a line, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the slope and the point (2, -3), we get (y - (-3)) = ½(x - 2).

Simplifying, we obtain the equation y + 3 = ½(x - 2). To get into slope-intercept form, y = mx + b, multiply the right-hand side by ½ to get y + 3 = ½x - 1. Finally, subtract 3 from both sides to get the equation of the line: y = ½x - 4.

Answer 2

y=2x-7

Step-by-step explanation:

The easiest way to answer this would be by using the slope-intercept form equation, y=mx+b. In this case, we can use our given in information to plug in values and find the equation.

Firstly, let's assess what know and what we don't:

Given the point (2,-3), we know that x=2 and y=-3. Now the slope for a perpendicular line can be found using a negative reciprocal, since the product of the slopes of both lines should equal -1. Therefore the slope must be 2.

All that's left is b, the y-intercept. To solve for this, we simply plug in what we have.

y=mx+b

-3=2(2)+b

-3=4+b

-3-4=b

-7=b

Now that we have b, we can write the equation:

y=2x-7