1. Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula

2. The point-slope formula is given by where m is the slope of the line and is a known point on the line.

3. Writing an Equation of a Line Using the Point-Slope Formula m = 3 Point ( -2, -4 ) The point-slope formula: -43 -2-4 3 -2 Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y. y + 4 = 3(x + 2) Apply the distributive property y + 4 = 3x + 6 Subtract 4 from both sides. y + 4 – 4 = 3x + 6 -4 Slope-intercept form y = 3x +2

4. Writing an Equation of a Line Through Two Points Points (-2, 5) and (4, -1) The point-slope formula: 5 4 5 -2 Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y. y – 5 = -1(x – (-2) Apply the distributive property y - 5 = -x + 2 Add 5 to both sides. y -5 + 5 = -x + 2 +5 Slope-intercept form y = -x + 3 Find the slope -2 5 4 -2

5. Write an Equation of a Line Parallel to Another Line Use the point-slope formula to find an equation of the line passing through the point(-1, 0) and parallel to the line y = -4x + 3, Write the final answer in slope-intercept form. Lets now apply the point-slope formula using m = -4 point = (-1, 0) -40 y = -4( x +1) y = -4x -4 Lets use the graph to find the equation. What is the slope and the y-intercept? What formula could we use to write the equation? Slope-intercept form y = mx + b m = -4 b = -4 y = mx + b y = -4x -4

6. Write an Equation of a Line Perpendicular to Another Line Use the point-slope formula to find an equation of the line passing through the point (-3, 1) and perpendicular to the line 3x + y = -2. Write the final answer in slope-intercept form. The given line can be written in slope-intercept form as y = -3x -2. The slope of this line is -3. Therefore, the slope of a line perpendicular to the given line is ⅓ (-3) 1⅓ Point-slope formula Substitute m = ⅓ x₁ = -3, y₁ = 1 To write the final answer in slope-intercept form, simplify the equation and solve for y. y – 1 = ⅓(x + 3) Apply the distributive property y - 1 = ⅓x + 1 Add 1 to both sides y = ⅓x + 2

7. FormEquationComments Standard form Ax + By = C 4x + 2y = 8A and B must not both be zero Horizontal Line y = k (k is a constant) y = 4The slope is zero and the y- intercept is (0, k). Vertical line x = h (h is a constant) x = -1The slope is undefined, and the x-intercept is (h, 0) Slope-intercept Form y = mx + b The slope is m y-intercept is (0, b) y = -3x +7 Slope = -3 y-intercept is (0, 7) Solving a linear equation for results in slope-intercept form. The coefficient of the x-term is the slope, and the constant defines the location of the y- intercept. Point-Slope Formula y - y₁ = m(x - x₁) m = -3 (x₁, y₁) = (4, 2) y – 2 = -3(x – 4) This formula is typically used to build an equation of a line when a point on the line is known and the slope of the line is known Different forms of Linear Equations: