Algebra 2Lesson 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 – y1 = m(x – x1)

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 = ½b = -5 y = ½ x – 5

Writing an Equation from a Graph

m=b=

m=b=

Writing an Equation In Slope-Intercept FormGiven 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 + bWhat you are given:

(2, -4)m = -3 -4 = (-3)(2) + b

-4 = -6 + b

2 = b y = -3x + 2

Writing an Equation In Slope-Intercept FormGiven 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 FormGiven 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 FormGiven 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 FormGiven 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:

2 1

2 1

slopey y

mx x

-= =

-

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 FormGiven two points

Problem: Write the equation of a line passing through the points (-3, 5) and (2, 2)

2 1

2 1

slopey y

mx x

-= =

- y = mx + b

Writing an Equation In Slope-Intercept FormGiven two points

Problem: Write the equation of a line passing through the points (-2, -3) and (0, 5)

2 1

2 1

slopey y

mx x

-= =

- y = mx + b

Writing an Equation In Slope-Intercept FormGiven 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.

2 1

2 1

slopey y

mx x

-= =

- y = mx + b

Writing an Equation In Slope-Intercept FormGiven 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.

2 1

2 1

slopey y

mx x

-= =

- y = mx + b

Writing an Equation In Slope-Intercept FormPassing 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 + bB

Am

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 FormPassing 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 + bB

Am

Writing an Equation In Slope-Intercept FormPassing 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 + bB

Am

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 FormPassing 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 + bB

Am