How do you find the equation of a line that is perpendicular and passing through a given point?

How do you find the equation of a line that is perpendicular and passing through a given point?

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

How do you find a perpendicular line that passes through the origin?

If the line passes through the origin, then you know that (0,0) is on the line. If the line is perpendicular to y=2x+3 then we know the line has slope m=−0.5. This is the negative reciprocal of the slope. The solution can be obtained by solving y=−0.5x+b using the information given.

What is the equation of a line that is perpendicular to − x 2y 4 and passes through the point − 2 1 )? Enter your equation in the box $\ text basic }$?

taking perpendicular at x=0, y=2 the eqn of the line perpendicular to -x+2y=4 is x+2y=0. hence the equation of the line passing through -2,1 is x+2y=3.

What is the slope of a line perpendicular to x 2y 4?

So the slope of the given line is m=12 . m*=−11/2=−2 .

What is a line that passes through the origin?

The slope intercept form is y = mx + b, where b is the y-intercept. In the equation y = 2x – 1, the y-intercept is -1. So, if you have an equation like y = 4x, there is no “b” term. Therefore, the y-intercept is zero, and the line passes through the origin.

Which equations represent the line that is perpendicular to the line?

For a line to be perpendicular to this line, the slope will be the negative inverse of 2x. If we start with line y=mx+b a line perpendicular to this would be y = – 1/m x + b. Since our line is y = 2x – 3.5, our perpendicular line will be y = – 1/2x +b.

How to find the slope of a perpendicular line in slope intercept form?

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2 x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2 x + b and solving for b, we get b = 6.

How to find the y-intercept of a line?

Solving with One Point and an Equation Download Article 1 Simplify the equation of the line. 2 Calculate the opposite reciprocal of the slope. When a line is perpendicular to another line, the slope will be the… 3 Plug the point into the slope equation to find the y-intercept. Now that you have the slope of the perpendicular… More

How to find the equation of a perpendicular line with two points?

Before you calculate the equation of the perpendicular line, you will need to find the slope of the line that crosses the two points. The equation for finding the slope of a line with two points is m = y 2 − y 1 x 2 − x 1 {\\displaystyle m={\\frac {{y^{2}}-{y^{1}}}{{x^{2}}-{x^{1}}}}} .

How do you find the equation with a slope of 2?

Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be – 1: So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3.