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Linear Equations & Functions Homework Solutions

Learn and practice writing linear equations in point-slope form, analyzing slopes, and constructing scatterplots. This session focuses on solving linear functions and arithmetic sequences.

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Linear Equations & Functions Homework Solutions

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  1. Do Now 11/15/18 • Take out HW from last night. • Text p. 179, #4-30 evens. • Copy HW in your planner. • Text p. 185, #4-30 evens, 40 • In your notebook, answer the following. Yesterday, you learned how to write an equation in slope-intercept form when given the slope and y-intercept of a line. Can you write an equation of a line with a slope of 2 and that passes through the point (4,-3)? The point (4,-3) is NOT the y-intercept and therefore, the answer cannot be y = 2x – 3.

  2. Homework Text p. 179, #4-30 evens

  3. Homework Text p. 179, #4-30 evens

  4. Learning Goal • Students will be able to write and solve linear functions, construct scatterplots, analyze lines of fit, and write arithmetic sequences Learning Target • Students will be able to write equations in point-slope form

  5. Slope Review The slope m of a line passing through two points and is the ratio of the rise change to the run. y run rise x

  6. Section 4.2 “Writing Linear Equations in Point-Slope Form” POINT-SLOPE FORM- of a linear equation is written as: y run y-coordinate point 1 x-coordinate point 1 rise slope x

  7. Write an equation in point-slope form of the line that passes through the point (4, -3) and has a slope of 2. STEP1 Write point-slope form STEP2 Substitute for the slope and the coordinates of the given point in Write point-slope form. Substitute 2 for m, 4 for x, and -3 for y. STEP3 Write an equation of the line in point-slope form. Write in point-slope.

  8. Write an equation in slope-intercept form of the line that passes through the point (-1, 4) and has a slope of -2. STEP1 Write point-slope form STEP2 Substitute for the slope and the coordinates of the given point in Write point-slope form. Substitute -2 for m, -1 for x, and 4 for y. STEP3 Write an equation of the line in slope-intercept form. Distributive property. Simplify. Write in slope-intercept form.

  9. y2– y1 4–3 1 m = = = x2–x1 4 – 2 2 Write an equation in point-slope formof the line that passes through (2, 3)and(4, 4). STEP1 Calculate the slope. STEP2 Substitute for the slope and the coordinates of the given point in Write point-slope form. or

  10. y y2– y1 3–1 2 m = = = x2 –x1 -1– 1 -2 Write an equation in slope-intercept formof the line shown. STEP1 Calculate the slope. = -1 x Substitute for the slope and the coordinates of the given point in STEP2 Write point-slope form. or STEP3 Write an equation of the line in slope-intercept form. Distributive property. Simplify. Write in slope-intercept form.

  11. On your own. Write an equation in slope-intercept form of the line that passes through (1, 4) and (3, 10). Write a linear function g with the values g(2) = 3 and g(6) =5.

  12. Because the equation is in point-slope form, you know that the line has a slope of and passes through the point (3, –2). 2 3 Graph the equation. Plot the point (3, – 2). Find a second point on the line using the slope. Draw a line through both points.

  13. Graph the equation. Because the equation is in point-slope form, you know that the line has a slope of –1 and passes through the point (2, 1). Plot the point (2, 1). Find a second point on the line using the slope. Draw a line through both points.

  14. The student council is ordering customized foam hands to promote school spirit. The table shows the cost of ordering different numbers of foam hands. Can the situation be modeled by a linear equation? Explain. If possible, write a linear model that represents the cost as a function of the number of foam hands. Write point-slope form. Simplify to slope-intercept form. Substitute 6 for m, 4 for x, and 34 for y.

  15. POINT-SLOPE FORM- of a linear equation is written as: What Did We Learn Today? y run y-coordinate point 1 x-coordinate point 1 rise slope x

  16. Homework • Text p. 185, #4-30 evens, 40

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