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- 1. Equations For Lines
- 2. Objective The student will be able to: <ul><li>write equations using slope-intercept form. </li></ul><ul><li>identify slope and y-intercept from an equation. </li></ul>
- 3. y = mx + b <ul><li>The equation is called the slope intercept form for a line. </li></ul><ul><li>The graph of this equation is a straight line. </li></ul><ul><li>The slope of the line is m. </li></ul><ul><li>The line crosses the y-axis at b . </li></ul><ul><li>The point where the line crosses the y-axis is called the y-intercept. </li></ul><ul><li>The (x,y) coordinates for the y-intercept are (0,b) </li></ul>
- 4. Y = mx+ b <ul><li>If your slope is positive the line will go up hill. </li></ul><ul><li>If your slope is negative the line will go down hill. </li></ul><ul><li>Remember we read from left to right. </li></ul><ul><li>Also, the slope is the m value. </li></ul><ul><li>Slope is RISE over RUN written as a fraction. </li></ul><ul><li>If the m is a whole number put it over one to form a fraction. </li></ul>
- 5. Types of lines <ul><li>1. All lines are straight. </li></ul><ul><li>2. They can be horizontal, vertical, or diagonal. </li></ul>
- 6. Graphing lines using the equation <ul><li>Identify the Y-intercept (b) and graph it on the y-axis with a point. </li></ul><ul><li>Identify what the slope is (m) . Remember slope is rise over run. </li></ul><ul><li>From the point on the y-axis, if your slope is positive go up or if it is negative go down whatever the RISE is. Go over to the right for the run. Mark the spot with a point. </li></ul><ul><li>Draw a line thru those two points </li></ul>
- 7. This is one of the big concepts in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept
- 8. When asked to write an equation, you need to know two things – slope (m) and y-intercept (b). There are three types of problems you will face.
- 9. Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. To write an equation, you need two things: slope (m) = y – intercept (b) = We have both!! Plug them into slope-intercept form y = mx + b 2 6 y = 2x + 6
- 10. Write the equation of a line that has a y-intercept of -3 and a slope of -4. <ul><li>y = -3x – 4 </li></ul><ul><li>y = -4x – 3 </li></ul><ul><li>y = -3x + 4 </li></ul><ul><li>y = -4x + 3 </li></ul>
- 11. Write an equation of the line that has a slope of 3 and goes through the point (2,1). To write an equation, you need two things: slope (m) = y – intercept (b) = We have to find the y-intercept!! Plug in the slope and ordered pair into y = mx + b 3 ??? 1 = 3(2) + b
- 12. 1 = 3(2) + b Solve the equation for b 1 = 6 + b -6 -6 -5 = b To write an equation, you need two things: slope (m) = y – intercept (b) = y = 3x - 5 3 -5
- 13. Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2). </li></ul><ul><li>To write an equation, you need two things: </li></ul><ul><li>slope (m) = </li></ul><ul><li>y – intercept (b) = </li></ul><ul><li>We need both!! First, we have to find the slope. Plug the points into the slope formula. </li></ul><ul><li>Simplify </li></ul>??? ???
- 14. Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2). </li></ul><ul><li>To write an equation, you need two things: </li></ul><ul><li>slope (m) = </li></ul><ul><li>y – intercept (b) = </li></ul><ul><li>It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use? </li></ul>???
- 15. 2 = (4) + b Solve the equation for b 2 = + b b = 4/3 To write an equation, you need two things: slope (m) = y – intercept (b) = 4/3
- 16. Write an equation of the line that goes through the points (0, 1) and (1, 4). <ul><li>y = 3x + 4 </li></ul><ul><li>y = 3x + 1 </li></ul><ul><li>y = -3x + 4 </li></ul><ul><li>y = -3x + 1 </li></ul>
- 17. To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. <ul><li>Find the slope and y-intercept. </li></ul><ul><li>y = 3x – 7 </li></ul><ul><li>y = m x + b </li></ul><ul><li>m = 3, b = -7 </li></ul>
- 18. Find the slope and y-intercept. <ul><li>2) y = x </li></ul><ul><li>y = m x + b </li></ul><ul><li>y = x + 0 </li></ul><ul><li>3) y = 5 </li></ul><ul><li>y = m x + b </li></ul><ul><li>y = 0x + 5 </li></ul>m = b = 0 m = 0 b = 5
- 19. Find the slope and y-intercept. 4) 5x - 3y = 6 <ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>5x – 3y = 6 </li></ul><ul><li>-3y = -5x + 6 </li></ul><ul><li>y = x - 2 </li></ul>-3 -3 -3 m = b = -2
- 20. Find the slope and y-intercept of y = -2x + 4 <ul><li>m = 2; b = 4 </li></ul><ul><li>m = 4; b = 2 </li></ul><ul><li>m = -2; b = 4 </li></ul><ul><li>m = 4; b = -2 </li></ul>

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