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Graph a line and write a linear equation using point-slope form.

Objectives. Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

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Graph a line and write a linear equation using point-slope form.

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  1. Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

  2. If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3and contains (2, 1) . Let (x, y) be any other point on the line. Substitute into the slope formula. Multiply both sides by (x - 2). Simplify.

  3. Additional Example 1A: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. y – y1= m(x – x1) Write the point-slope form.

  4. Additional Example 1B: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. slope = –4; (0, 3)

  5. Additional Example 1C: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. slope = 1; (–1, –4)

  6. Check It Out! Example 1b Write an equation in point slope form for the line with the given slope that contains the given point. slope = 0; (3, –4)

  7. In Lesson 5-7, you graphed a line given its equation in slope-intercept form. You can also graph a line when given its equation in point-slope form. Start by using the equation to identify a point on the line. Then use the slope of the line to identify a second point.

  8. Additional Example 2A: Using Point-Slope Form to Graph Graph the line described by the equation. y – 1 = 2(x – 3) (2,5) y – 1= 2(x – 3) is in the form y – y1= m(x – x1). (1,3) The line contains the point (3, 1). Step 1 Plot (3, 1). Step 2 Count 2 units upand 1 unit rightand plot another point. Step 3 Draw the line connecting the two points.

  9. Additional Example 2B: Using Point-Slope Form to Graph Graph the line described by the equation.

  10. Additional Example 2C: Using Point-Slope Form to Graph Graph the line described by the equation. y + 3 = 0(x – 4)

  11. Check It Out! Example 2a Graph the line described by the equation. y + 2 = –(x – 2)

  12. + 4 + 4 Additional Example 3A: Writing Linear Equations in Slope-Intercept Form Write the equation that describes each line in slope-intercept form. Slope = 3, (–1, 4) is on the line. Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y –4 = 3(x + 1) Distribute 3 on the right side. y – 4 = 3x + 3 Add 4 to both sides. y = 3x +7

  13. Additional Example 3B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. (2, –3) and (4, 1)

  14. Additional Example 3C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form.

  15. Check It Out! Example 3a Write the equation that describes the line in slope-intercept form.

  16. Check It Out! Example 3b Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10)

  17. Additional Example 4: Using Two Points Find Intercepts Write an equation in slope-intercept form for the line through (10, –3) and (5, –2).

  18. Check It Out! Example 4 Write an equation in slope-intercept form for the line through the two points. (2, 15) and (–4, –3)

  19. y + 6 = (x – 3) y = x + 4 Lesson Quiz Write an equation in slope-intercept form for the line with the given slope that contains the given point. 1. Slope = –1; (0, 9) y − 9 = –(x − 0) 2. Slope = ; (3, –6) Write an equation that describes each line the slope-intercept form. 3. Slope = –2, (2, 1) is on the line y = –2x + 5 4. (0, 4) and (–7, 2) are on the line

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