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How do you find the equation of intersection of two lines?

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How do you find the equation of intersection of two lines?

FAQs on Intersection of Two Lines

  1. Get the two equations for the lines into slope-intercept form.
  2. Set the two equations for y equal to each other.
  3. Solve for x.
  4. Use this x-coordinate and substitute it into either of the original equations for the lines and solve for y.

How do you find the intersection of two lines in a quadratic equation?

Subtract mx+d from both sides. Now we have a quadratic equation in one variable, the solution of which can be found using the quadratic formula. The solutions to the equation ax2+(b−m)x+(c−d)=0 will give the x-coordinates of the points of intersection of the graphs of the line and the parabola.

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What is an equation of the line that passes through?

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line. Fill in one of the points that the line passes through…

How do you find the intersection of two lines using substitution?

  1. Step 1 : First, solve one linear equation for y in terms of x .
  2. Step 2 : Then substitute that expression for y in the other linear equation.
  3. Step 3 : Solve this, and you have the x -coordinate of the intersection.
  4. Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.

How do you find the intersection between a line and a parabola?

A line can meet a parabola in at most two points. If the discriminant of the resulting quadratic is negative, the line does not meet the parabola at all. If the discriminant of the resulting quadratic is positive, the line meets the parabola in two distinct points.

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How do you find the equation of a line that has the given slope and passes through the given point?

These are the two methods to finding the equation of a line when given a point and the slope:

  1. Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b.
  2. Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.