2.4 – Writing Linear Equations

2.4 – Writing Linear Equations

Forms:

2.4 – Writing Linear Equations

Forms: Standard Form

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = C

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = C

Slope-Intercept Form

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = C

Slope-Intercept Form y = mx + b

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = C

Slope-Intercept Form y = mx + b

Point-Slope Form

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = C

Slope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = C

Slope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a Point

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given:

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1)

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1)

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + b

Point-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1) y – 1 = (-3/2)(x – (-

4))

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + bPoint-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1) y – 1 = (-3/2)(x – (-

4)) y – 1 = (-3/2)(x + 4)

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + bPoint-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1) y – 1 = (-3/2)(x – (-

4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + bPoint-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1) y – 1 = (-3/2)(x – (-

4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + bPoint-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6 + 1 + 1

2.4 – Writing Linear Equations

Forms: Standard Form Ax + By = CSlope-Intercept Form y = mx + bPoint-Slope Form y – y1 = m(x – x1)

Example 1 - Write an Equation Given Slope & a PointWrite and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).Given: m = -3/2

(-4,1) Point-Slope y – y1 = m(x – x1) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6 + 1 + 1 y = (-3/2)x – 5

Example 2 Write an Equation of a Perpendicular Line

Example 2 Write an Equation of a Perpendicular Line

Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

Example 2 Write an Equation of a Perpendicular Line

Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3)

Example 2 Write an Equation of a Perpendicular Line

Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

Example 2 Write an Equation of a Perpendicular Line

Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

Example 2 Write an Equation of a Perpendicular Line

Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

Example 2 Write an Equation of a Perpendicular Line

Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

y – y1 = m(x – x1)

Example 2 Write an Equation of a Perpendicular LineWrite an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

y – y1 = m(x – x1)y – 3 = ¼(x – (-4))

Example 2 Write an Equation of a Perpendicular LineWrite an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

y – y1 = m(x – x1)y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4)

Example 2 Write an Equation of a Perpendicular LineWrite an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.y – y1 = m(x – x1)y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4)y – 3 = ¼(x) + ¼(4)

Example 2 Write an Equation of a Perpendicular LineWrite an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

y – y1 = m(x – x1)y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4)y – 3 = ¼(x) + ¼(4) y – 3 = ¼(x) + 1

Example 2 Write an Equation of a Perpendicular LineWrite an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

y – y1 = m(x – x1)y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4)y – 3 = ¼(x) + ¼(4) y – 3 = ¼(x) + 1 + 3 + 3

Example 2 Write an Equation of a Perpendicular LineWrite an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

(-4,3) m1 = -4

m2 = ¼

So, write eq. through (-4,3) w/m2 = ¼.

y – y1 = m(x – x1)y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4)y – 3 = ¼(x) + ¼(4) y – 3 = ¼(x) + 1 + 3 + 3 y = ¼(x) + 4