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Published byClinton Houston Modified over 8 years ago

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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.

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Suppose the slope of a line is 5 and the y- intercept is 2. How would 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

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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

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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)x + 1

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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

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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.

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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

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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

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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 + bSubtract 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

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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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