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5.1 Writing Linear Equations in Slope-Intercept Form 5.2 Writing Linear Equations Given the Slope and a Point

5.1 Writing Linear Equations in Slope-Intercept Form 5.2 Writing Linear Equations Given the Slope and a Point. Quick Review. An equation of a line can be written in slope-intercept form y = mx + b where m is the slope and b is the y-intercept.

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5.1 Writing Linear Equations in Slope-Intercept Form 5.2 Writing Linear Equations Given the Slope and a Point

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  1. 5.1 Writing Linear Equations in Slope-Intercept Form5.2 Writing Linear Equations Given the Slope and a Point

  2. Quick Review • An equation of a line can be written in slope-intercept form y = mx + b where m is the slope and b is the y-intercept. • The y-intercept is where a line crosses the y-axis.

  3. Writing an Equation of a Line • Suppose the slope of a line is 5 and the y-intercept is 2. How would this you write the equation of this line in slope-intercept form? • First write the slope-intercept form. y = mx + b • Now substitute 5 for m and 2 for b. y = 5x + 2

  4. Write the Equation of a Line from a Graph • Where does the line cross the y-axis? • At the point (0, -4) • The y-intercept is -4. • What is the slope of the line? • The graph also crosses the x-axis at (2, 0). • We can use the slope formula to find our slope. m = -4 – 0 = -4 = 2 0 – 2 -2 We know our slope is 2 and our y-intercept is -4, what is the equation of our line? y = mx + b y = 2x + (-4) y = 2x -4

  5. Let’s try some examples! • Write the equation of a line with a slope of -2 and a y-intercept of 6. • y = mx + b • y = -2x + 6 • Write the equation of a line with a slope of -4/3 and a y-intercept of 1. • y = mx + b • y = (-4/3) + 1

  6. Using a graph • Where does the line cross the y-axis? • At the point (0, 2) • So the y-intercept b is 2. • The line also passes through the point (3, 0). • We can use these points to find the slope of the line. How? What formula do we use? • Using the slope formula, we find that the slope m is -2/3. • Write the equation of the line. • y= mx + b • y = (-2/3)x + 2

  7. If we are given the Slope and a Point • Step 1: • First find the y-intercept. Substitute the slope m and the coordinates of the given point (x, y) into the slope-intercept form, y = mx + b. Then solve for the y-intercept b. • Step 2: • Then write the equation of the line. Substitute the slope m and the y-intercept b into the slope-intercept form, y = mx + b.

  8. If We Are Given the Slope and a Point • Suppose we have a slope of -3 and it passes through the point (1, 2). • We first need to find the y-intercept. We can do this by substituting our information into slope-intercept form and solving for b. • y = mx + b • 2 = -3(1) + b • 2 = -3 + b Add 3 to both sides. • 5 = b Now we know that the y-intercept is 5. • y = mx + b • y = -3x + 5

  9. Try These! • Suppose we have a line with a slope of -1 and passes through the point (3, 4). • y = mx + b • 4 = (-1)3 + b • 4 = -3 + b • 7 = b • y = mx + b • y = (-1)x + 7 • y = -x + 7 • Suppose we have a line with a slope of 2 and passes through the point (1, 3). • y = mx + b • 3 = 2(1) + b • 3 = 2 + b • 1 = b • y = mx + b • y = 2x + 1

  10. Writing Equations of Parallel Lines • Two nonvertical lines are parallel if and only if they have the same slope. • Write the equation of a line that is parallel to the line y = 4x -3 and passes through the point (3, 2). • Since the two lines are parallel then both lines have a slope of m = 4. • We must substitute the slope and coordinates into the slope-intercept form and solve for b. • 2 = 4(3) + b • 2 = 12 + b Subtract 12 from both sides • -10 = b • Now we have enough information to write the equation of the line. • y = mx + b • y = 4x + (-10) • y = 4x -10

  11. Almost done! • Write the equation of a line that is parallel to the line y = -2x -3 and passes through the point ( -2, 3). • Since they are parallel, they both have the same slope m of -2. • Now substitute our slope and coordinates into slope-intercept form. • 3 = -2(-2) + b • 3 = 4 + b • -1 = b • Now we can write the equation of the second line. • y = mx + b • y = -2x -1 • Write the equation of a line that is parallel to the line y = 3x + 2 and passes through the point (4, -1). • Since they are parallel, they both have the same slope m of 3. • Now substitute our slope and coordinates into slope-intercept form. • -1 = 3(4) + b • -1 = 12 + b • -13 = b • Now we can write the equation of the second line. • y = mx + b • y = 3x -13

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