2.4 – Writing Linear Equations. 2.4 – Writing Linear Equations Forms:
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Transcript of 2.4 – Writing Linear Equations. 2.4 – Writing Linear Equations Forms:
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
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