Algebra 2 Lesson 2-4 Writing Linear Equations

Different Forms of Linear Equations Slope-intercept Form: y = mx + b Standard Form: Ax + By = C Point-Slope Form: y – y 1 = m(x – x 1 )

Slope-Intercept Form y = mx + b (x,y) is a point on the line m is the slope of the line (rise/run) b is the y-intercept (where your line crosses the y-axis)

Writing an Equation In Slope-Intercept Form Given the slope and the y-intercept Problem: Write the equation of a line with a y-intercept of -5 and a slope of 1/2. y = mx + b m = ½ b = -5 y = ½ x – 5

Writing an Equation from a Graph m=b=m=b= m=b=m=b=

Writing an Equation In Slope-Intercept Form Given the slope and a point on the line Problem: Write the equation of a line passing through the point (2, -4) with a slope of -3. y = mx + b What you are given: (2, -4) m = = (-3)(2) + b -4 = -6 + b 2 = b y = -3x + 2

Writing an Equation In Slope-Intercept Form Given the slope and a point on the line Problem: Write the equation of a line passing through the point (16, -3) with a slope of 1/4. y = mx + b

Writing an Equation In Slope-Intercept Form Given the slope and a point on the line Problem: Write the equation of a line passing through the point (-7, 5) with a slope of 6. y = mx + b

Writing an Equation In Slope-Intercept Form Given the slope and a point on the line Problem: Write the equation of a line passing through the point (-5, 1) with a slope of 3/2. y = mx + b

Writing an Equation In Slope-Intercept Form Given two points Problem: Write the equation of a line passing through the points (6, 1) and (8, -4)  Find the slope given the 2 points using the formula:  Use the slope and one of the points to find the y-intercept.  Use the slope and y-intercept to write the equation. y = mx + b

Writing an Equation In Slope-Intercept Form Given two points Problem: Write the equation of a line passing through the points (-3, 5) and (2, 2) y = mx + b

Writing an Equation In Slope-Intercept Form Given two points Problem: Write the equation of a line passing through the points (-2, -3) and (0, 5) y = mx + b

Writing an Equation In Slope-Intercept Form Given the x-intercept and y-intercept Problem: Write the equation of a line with an x-intercept of 5 and a y-intercept of -4. y = mx + b

Writing an Equation In Slope-Intercept Form Given the x-intercept and y-intercept Problem: Write the equation of a line with an x-intercept of -6 and a y-intercept of -2. y = mx + b

Writing an Equation In Slope-Intercept Form Passing through a point and parallel to a line Problem: Write the equation of a line passing through the point (2, 5) parallel to the line 6x - 3y = 5. y = mx + b  Find the slope of the given line.  Use the slope and the point to find the y-intercept.  Use the slope and y-intercept to write the equation.

Writing an Equation In Slope-Intercept Form Passing through a point and parallel to a line Problem: Write the equation of a line passing through the point (-4, 7) parallel to the line 4x + 2y = 23. y = mx + b

Writing an Equation In Slope-Intercept Form Passing through a point and perpendicular to a line Problem: Write the equation of a line passing through the point (2, -5) perpendicular to the line x - 4y = 28 y = mx + b  Find the slope of the given line.  Use the slope and the point to find the y-intercept.  Use the slope and y-intercept to write the equation.  Find the opposite reciprocal of the slope you just found.

Writing an Equation In Slope-Intercept Form Passing through a point and perpendicular to a line Problem: Write the equation of a line passing through the point (5, 2) perpendicular to the line x + 3y = 7 y = mx + b