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# Chapter 6.1 6.2

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### Transcript

• 1. &#xF09E; &#xF09E; An equation of a line can be written in slopeintercept form y = mx + b where m is the slope and b is the yintercept. The y-intercept is where a line crosses the yaxis.
• 2. &#xF097; Suppose the slope of a line is 5 and the yintercept is 2. How would this you write the equation of this line in slope-intercept form? &#xF097; First write the slope-intercept form. y = mx + b &#xF097; Now substitute 5 for m and 2 for b. y = 5x + 2
• 3. &#xF097; &#xF097; y = mx + b y = 2x + (-4) y = 2x -4 Where does the line cross the y-axis? &#x25E6; At the point (0, -4) &#x25E6; The y-intercept is -4. What is the slope of the line? &#x25E6; The graph also crosses the x-axis at (2, 0). &#x25E6; We can use the slope formula to find our slope. m = -4 &#x2013; 0 = -4 = 2 0 &#x2013; 2 -2 We know our slope is 2 and our y-intercept is -4, what is the equation of our line?
• 4. &#xF09E; Write the equation of a line with a slope of -2 and a y-intercept of 6. &#xF0A2; &#xF0A2; y = mx + b y = -2x + 6 &#xF09E; Write the equation of a line with a slope of -4/3 and a y-intercept of 1. &#xF0A2; &#xF0A2; y = mx + b y = (-4/3) + 1
• 5. &#xF097; Where does the line cross the y-axis? &#x25E6; &#x25E6; &#xF097; &#xF097; 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? &#x25E6; &#x25E6; Using the slope formula, we find that the slope m is -2/3. Write the equation of the line. &#xF09E; &#xF09E; y= mx + b y = (-2/3)x + 2
• 6. &#xF09E; Step 1: &#xF0A1; 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. &#xF09E; Step 2: &#xF0A1; Then write the equation of the line. Substitute the slope m and the y-intercept b into the slopeintercept form, y = mx + b.
• 7. &#xF097; Suppose we have a slope of -3 and it passes through the point (1, 2). &#x25E6; We first need to find the y-intercept. We can do this by substituting our information into slope-intercept form and solving for b. &#xF09E; &#xF09E; &#xF09E; &#xF09E; y = mx + b 2 = -3(1) + b 2 = -3 + b 5=b is 5. &#xF09E; &#xF09E; y = mx + b y = -3x + 5 Add 3 to both sides. Now we know that the y-intercept
• 8. &#xF09E; Suppose we have a line with a slope of -1 and passes through the point (3, 4). &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; y = mx + b 4 = (-1)3 + b 4 = -3 + b 7=b y = mx + b y = (-1)x + 7 y = -x + 7 &#xF09E; Suppose we have a line with a slope of 2 and passes through the point (1, 3). &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; &#xF0A2; y = mx + b 3 = 2(1) + b 3=2+b 1=b y = mx + b y = 2x + 1
• 9. &#xF097; Write an equation f the line that passes through (-2,5) and (2,1).