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Uploaded byJessica Garcia
Writing linear equations
This document discusses writing linear equations in slope-intercept form and point-slope form by given information such as the slope, y-intercept, or two points on the line. It provides examples of finding the equation of a line given its slope and y-intercept, two points, or one point and the slope. The key methods covered are using the slope-intercept form y=mx+b and point-slope form y-y1=m(x-x1).
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Introduction to writing linear equations, details on determining the equation from given graphs.
Introduction to writing linear equations, details on determining the equation from given graphs.
Explains the slope-intercept form (y = mx + b) and determining slope (m) and y-intercept (b).
Identifying slopes and y-intercepts from given equations, providing examples and calculations.
Finding equations using slope and a point as well as two points, utilizing point-slope form.
Using point-slope form to derive the equation of a line, demonstrated through calculation examples.
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Writing linear equations
- 1. Writing Linear EquationsUsing Slope Intercept Form Point-Slope Form.
- 2.
- 3. We’ve learned tograph given an equation. Now we’ll learn to write the equation given the graph There are three ways. It all depends on what information you are given as to which process you use.
- 4. Slope-Intercept Form y = mx + b [or f ( x ) = mx + b ] m is the slope b is the y -intercept
- 5. Find the Equationof the Line What is the y -intercept? b = -2 What is m ? m = y = x -2 x y
- 6. Find the Equationof the Line b = ? b = 1 m = ? m = - y = - x + 1 x y
- 7. Find the Equationof the Line b = ? b = 4 m = ? m = 0 y = 0 x + 4 y =4 x y
- 8. Find the Slopeand y-intercept of each Equation: 1) y = -4 x + 3 m = -4 b = 3 2) y = 5 - x m = - b = 5 3) 8 x + y = m = -8 b = 4) 4 x - 2 y = 10 m = 2 b = -5
- 9. Find the EquationGiven the Slope and y -intercept 1) m = -3, b = 1 y = -3 x + 1 2) m = - , b = -4 y = - x - 4
- 10. Find the EquationGiven the Slope and a Point Given m = -1, (2, 1) First, calculate b by substituting the slope and the coordinates into y = mx + b. y = -1 x + b 1 = -1(2) + b 1 = -2 + b 3 = b y = -1 x + 3
- 11. If you aregiven two points on the line Find the slope using the two points Then plug this slope and either one of the points into the point slope formula.
- 12. Find the EquationGiven Two Points Given (-1, 3) and (2, 1) First, calculate the slope: Second, find b . Use either point... m = , (2, 1) 1 = (2) + b 1 = + b = b
- 13. Use Point SlopeForm: If you are given slope, m, and a point (x 1 ,y 1 ) on the line y – y 1 = m ( x – x 1 )
- 14. Write an equationof a line containing the point (1,2) with slope of -1/2. Use (x 1 ,y 1 ) = (1,2) & m = -1/2 y – 2 = -1/2 ( x – 1) Now you can simplify to the slope intercept form y – 2 = -1/2 x + ½ y = -1/2 x + 5/2
- 15. Given two points(-2,2) & (3,7) Find the slope: m=1 Plug this slope and one of the points into the point slope formula. y – 2 = 1 ( x – (-2)) y – 2 = x + 2 y = x + 4 (put the equation into slope intercept form) (-2,2) (3,7)