Linear EquationsSlope-Intercept Form | Point-Slope Form | Horizontal & Vertical Lines

Learning Objectives• Determine the equation of a line given the

slope and y-intercept• Determine the equation of a line given the

slope and any point• Determine the equation of a line given any

two points on the line

Linear Equations

• Standard-form – an equation of a line in the form Ax + By = C– Value of A is greater than or equal to 0– Value of A and B are not both 0– Value of A, B, and C are real number constants

• Ex) 3x + 2y = 6– Subtract 3x from both sides of equation 2y = –3x

+ 6– Then, divide both sides of equation by 2 for

Slope-Intercept Form

• Lines can be graphed by identifying the transformations on the linear parent function, y = x – Ex)

• Reflected over the y-axis

• Vertically stretched • Vertically translated

up the y-axis by 3• (0,3) is the y-

intercept• Slope is –3/2

Slope-Intercept Form

• Equation can be written quickly if slope and y-intercept are known

• Slope and y-intercept recognized immediately in equation and line can be graphed quickly

Slope-Intercept Form

The slope-intercept form of an equation of a line is in the formy = mx + b

where m is the slope of the line, and b is the y-intercept.

Slope-intercept form of a line

• When a slope is given without a y-intercept, an equation can be formed from a point on the line– Must apply transformations to the linear parent

function until the equation represents the desired line• Ex) If slope is 1/2, then the graph of the linear parent

function should be vertically compressed

• If the point on the line is (4,5), then translate the point to the right by four units and up by five units

• Value of y for the given point can be moved to the other side of the equation

Point-Slope Form

• Advantages of point-slope form– Equation can be formed quickly from the slope

and one point of a line– Can find y-intercept by solving the equation for y

and converting the equation into slope-intercept form

Point-Slope Form

The point-slope form of the equation of a line isy – y1 = m(x – x1)

where m is the slope of the line, and (x1,y1) is a point on the line.

Point-slope form of a line

Point-Slope Form Example

Ex) A line passes through the following two points, (1,4) and (5,7). Find the equation of this line in point–slope form and slope–intercept form. Justify

Slope is located to the left of the x-value in each form

EvaluateDepending on

the information given, certain forms

can be created faster

AnalyzeFormulate

Find slope and substitute into

point–slope equation, solve for y

Determine

• Sometimes linear equations do not appear to contain both x- and y-components– Ex) y = 4

• Two points on the line are (–3,4) and (5,4)• Slope is

• Standard form is 0x + y = 4• Slope–intercept form is y = 0x + 4• Possible point–slope equation is y – 4 = 0(x – 5)

Horizontal & Vertical Lines

• Ex) x = 4– Two points on the

line are (4, –2) and (4,3)

– Slope is

– Impossible to write equation of a vertical line in slope–intercept or point–slope form

– Standard form is x + 0y = 4

Horizontal & Vertical Lines

Learning Objectives• Determine the equation of a line given the

slope and y-intercept• Determine the equation of a line given the

slope and any point• Determine the equation of a line given any

two points on the line

Linear Equations