1 / 14

Writing Equations of Lines in Slope-Intercept Form

Learn how to write equations of lines in slope-intercept form using given points and slopes, and how to determine parallel and perpendicular lines.

jcamille
Download Presentation

Writing Equations of Lines in Slope-Intercept Form

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Write an equation of the line in slope- intercept form. STEP 1 Find the slope. Choose two points on the graph of the line, (0, 4) and (3, –2). m – 2 = = = Find the y-intercept. The line intersects the y-axis at the point (0, 4), so the y-intercept is 4. STEP 2 4 – (– 2) 6 0 – 3 – 3 EXAMPLE 1 Write an equation of a line from a graph SOLUTION

  2. STEP 3 Write the equation. y mx + b = EXAMPLE 1 Write an equation of a line from a graph Use slope-intercept form. y = –2x + 4 Substitute – 2 for mand 4 for b.

  3. STEP 1 Find the slope m. The slope of a line parallel to y = 2x –3 is the same as the given line, so the slope is 2. STEP 2 Find the y-intercept bby using m=2 and (x, y)=(– 1, 1). EXAMPLE 2 Write an equation of a parallel line Write an equation of the line passing through the point (– 1, 1) that is parallel to the line with the equation y= 2x–3. SOLUTION

  4. y mx + b = EXAMPLE 2 Write an equation of a parallel line Use slope-intercept form. Substitute forx, y, and m. 1 = 2 (–1 ) + b 3 = b Solve for b. Because m = 2 and b = 3, an equation of the line is y = 2x+ 3.

  5. STEP 1 Find the slope mof line j. Line khas a slope of – 2. – 2 m = – 1 The product of the slopes of lines is –1. m = 1 2 EXAMPLE 3 Write an equation of a perpendicular line Write an equation of the line jpassing through the point (2, 3) that is perpendicular to the line kwith the equation y = – 2x + 2. SOLUTION Divide each side by – 2.

  6. mx + b y = ( 2 ) + b 3 = 1 1 2 2 EXAMPLE 3 Write an equation of a perpendicular line STEP 2 Find the y-intercept bby using m= and (x, y)=(2, 3). Use slope-intercept form. Substitute for x, y, and m. 2 = b Solve for b.

  7. Because m = and b = 2, an equation of line j is y=x+ 2. You can check that the lines jand kare perpendicular by graphing, then using a protractor to measure one of the angles formed by the lines. 1 1 2 2 EXAMPLE 3 Write an equation of a perpendicular line

  8. Write an equation of the line in the graph at the right. STEP 1 Find the slope of the line. 2 . m = = 3 1 – (– 1) Find the y-intercept. Since the line intersects the y-axis at the point (0, –1), so the y-intercept is –1. STEP 2 1 – 1 for Examples 1, 2 and 3 GUIDED PRACTICE SOLUTION

  9. STEP 3 Write the equation. y mx + b = 2 x y = – 1 Substitute for mand –1 for b. 3 2 3 for Examples 1, 2, and 3 GUIDED PRACTICE Use slope-intercept form.

  10. Write an equation of the line that passes through (– 2, 5) and (1, 2). STEP 1 Find the slope of the line. 5 – 2 3 m = = – 3 – 2 – 1 Find the y-intercept. Since the line intersects the y-axis at the point (– 2, 5) and (1, 2) , so the y-intercept is 3. STEP 2 for Examples 1, 2 and 3 GUIDED PRACTICE SOLUTION = –1

  11. y mx + b = EXAMPLE 1 for Examples 1, 2 and 3 GUIDED PRACTICE STEP 3 Write the equation. Use slope-intercept form. y = –x + 3 Substitute –1 for mand 3 for b.

  12. Write an equation of the line that passes through the point (1, 5) and is parallel to the line with the equation y=3x–5. Graph the lines to check that they are parallel. STEP 1 Find the slope of the line. The slope of the line parallel to y = 3x – 5 is the same as the given line. So , the slope is 3. Find the y-intercept b by using m= 3 and (x , y)= (1 , 5). STEP 2 for Examples 1, 2 and 3 GUIDED PRACTICE SOLUTION

  13. y mx + b = for Examples 1, 2 and 3 GUIDED PRACTICE Use slope-intercept form. y = 3 x + 2 STEP 3 Graph the lines.

  14. How do you know the lines x = 4 and y = 2 are perpendicular? x = 4 is a vertical line whiley = 2 is horizontal line. Hence x y. for Examples 1, 2 and 3 GUIDED PRACTICE SOLUTION

More Related