|
This Lesson (Find Equation of a Line given Slope and a Point) was created by by VirtualMathTutor(26)
  About VirtualMathTutor: An online math instructor who loves mathematics and believes in developing math skills one step at a time.
Example 1
Find the equation of a line (slope-intercept form) that has a slope of 4 and passing through the point (3, 2). Solution: To find our equation we will use the formula: y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point. In this example m = 4 x1 = 3 y1 = 2 Substitute the values into the formula: y � y1 = m(x � x1) y � 2 = 4(x � 3) Let�s simplify by expanding the right side of the equation. Multiply 4 by each term in the parentheses: y � 2 = 4x � 12 Since we want the equation in slope-intercept form, that is, in the form y = mx + b, we will have to solve for y. To solve for y, add 2 to both sides of the equation: y � 2 + 2 = 4x � 12 + 2 Simplify to get: y = 4x � 10 Example 2 Find the equation of a line (slope-intercept form) that has a slope of -1 and passing through the point (-2, 5). Solution: To find our equation we will use the formula: y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point. In this example m = -1 x1 = -2 y1 = 5 Substitute the values into the formula: y � y1 = m(x � x1) y � 5 = -1(x � (-2) ) Let�s simplify the right side of the equation: y � 5 = -1(x + 2) Simplify the right side of the equation further by multiplying each term in the parentheses by -1: y � 5 = -x � 2 Since we want the equation in slope-intercept form, that is, in the form,y = mx + b, we will have to solve for y. Add 5 to both sides of the equation: y � 5 + 5 = -x � 2 + 5 Simplify to get: y = -x + 3 Example 3 Find the equation of a line (slope-intercept form) that has a slope of Solution: To find our equation we will use the formula: y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point. In this example x1 = 0 y1 = -6 Substitute the values into the formula: y � y1 = m(x � x1) y � (-6) = Let�s simplify the left side and right side of the equation: y + 6 = Since we want the equation in slope-intercept form, that is, in the form,y = mx + b, we will have to solve for y. Subtract 6 from both sides of the equation: y + 6 - 6 = Simplify to get: y = Are you hanging in there with me? Recap: Use this formula to find equation of a line given slope and a point:y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point given. Let�s keep going! Example 4 Find the equation of a line (slope-intercept form) that has a slope of Solution: To find our equation we will use the formula: y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point. In this example y1 = 3 Substitute the values into the formula: y � y1 = m(x � x1) y � 3 = We will then have to expand the right side of the equation by multiplying each term in the parentheses by y � 3 = Since we want the equation in slope-intercept form, that is, in the form, y = mx + b, we will have to solve for y. Add 3 to both sides of the equation: y � 3 + 3 = Simplify to get: y = Wondering how we ended up getting We can rewrite this as: Then find the lowest common denominator (LCD) which is 16. Divide the LCD (16) by each denominator and multiply by the numerator: = Example 5 Find the equation of a line (slope-intercept form) that has a slope of 0 and passing through the point (-4, -2). Solution: To find our equation we will use the formula: y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point. In this example m = 0 x1 = -4 y1 = -2 Substitute the values into the formula: y � y1 = m(x � x1) y � (-2) = 0(x � (-4)) Let�s simplify the left side and right side of the equation: y + 2 = 0(x + 4) y + 2 = 0 Since we want the equation in slope-intercept form, that is, in the form,y = mx + b, we will have to solve for y. Subtract 2 from both sides of the equation: y + 2 - 2 = 0 - 2 Simplify to get: y = -2 (a horizontal line) Looks different from the equations we got in the first few examples? y = -2 is an equation of a horizontal line that runs through -2. Example 6 Find the equation of a line (slope-intercept form) that has an undefined slope and passing through the point (0, 3). Solution: Since the slope is undefined, the equation is of the form x = 0 which is a vertical line passing through the point (0, 3). TRY THIS: Try the following on your own. Don�t worry, I will provide some tips to help you along the way. Find the equation of a line (slope-intercept form) that has a slope of 2 and passing through the point (6, 0). Tips: � Don�t forget the formula: y � y1 = m(x � x1) � Remember to label your coordinates, so you do not mix the �x� and �y� values up � Insert the values of m, x1, and y1 into the formula � Solve for y What is the equation of the line? Did you get y = 2x - 12? If you did not, try retracing your steps; label your coordinates correctly before inserting the values in the formula. See explanation below: To find our equation we will use the formula: y � y1 = m(x � x1), where m is the slope and (x1, y1) is the point. In this example m = 2 x1 = 6 y1 = 0 Substitute the values into the formula: y � y1 = m(x � x1) y � 0 = 2(x � 6) Let�s simplify by expanding the right side of the equation: y � 0 = 2x � 12 Simplify to get: y = 2x - 12 For more fun math adventures, visit me on my blog at: http://www.virtual-mathematics.com/ <<<===--- just does not exist or website: http://www.my-virtual-math-tutor.com/ <<<===--- just does not exist This lesson has been accessed 84082 times. |
