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Graph Linear Equations: Step-by-Step Practice

Learn to graph linear equations step by step with examples and guided practice to plot x and y intercepts, draw lines, and understand horizontal and vertical lines.

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Graph Linear Equations: Step-by-Step Practice

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  1. EXAMPLE 4 Graph an equation in standard form Graph 5x + 2y = 10. SOLUTION STEP1 The equation is already in standard form. STEP2 Identify the x-intercept. Lety= 0. 5x + 2(0) = 10 x = 2 Solve for x. The x-intercept is 2. So, plot the point (2, 0).

  2. EXAMPLE 4 Graph an equation in standard form STEP3 Identify the y-intercept. Lety= 0. 5(0) + 2y = 10 y = 5 Solve for y. The y-intercept is 5. So, plot the point (0, 5). STEP4 Draw a line through the two points.

  3. EXAMPLE 5 Graph horizontal and vertical lines Graph (a) y = 2 and (b) x = – 3. SOLUTION a. The graph of y = 2 is the horizontal line that passes through the point (0, 2). Notice that every point on the line has a y-coordinate of 2. b. The graph of x = –3 is the vertical line that passes through the point (–3, 0). Notice that every point on the line has an x-coordinate of –3.

  4. for Examples 4 and 5 GUIDED PRACTICE Graph the equation. 11. 2x + 5y = 10 SOLUTION STEP1 The equation is already in standard form. STEP2 Identify the x-intercept. Lety= 0. 2x + 5(0) = 10 x = 5 Solve for x. The x-intercept is 5. So, plot the point (5, 0).

  5. for Examples 4 and 5 GUIDED PRACTICE STEP3 Identify the y-intercept. 2(0) + 5y = 10 Lety= 0. y = 2 Solve for y. The y-intercept is 5. So, plot the point (0, 2). STEP4 Draw a line through the two points.

  6. for Examples 4 and 5 GUIDED PRACTICE Graph the equation. 12. 3x – 2y = 12 SOLUTION STEP1 The equation is already in standard form. STEP2 Identify the x-intercept. Lety= 0. 3x – 2(0) = 12 x = 4 Solve for x. The x-intercept is 5. So, plot the point (4, 0).

  7. for Examples 4 and 5 GUIDED PRACTICE STEP3 Identify the y-intercept. 3(0) – 2y = 12 Lety= 0. y =–6 Solve for y. The y-intercept is 5. So, plot the point (0, –6). STEP4 Draw a line through the two points.

  8. for Examples 4 and 5 GUIDED PRACTICE Graph the equation. 13. x = 1 SOLUTION The graph of x = 1 is the vertical line that passes through the point (1, 0). Notice that every point on the line has an x-coordinate of 1.

  9. for Examples 4 and 5 GUIDED PRACTICE Graph the equation. 14. y = –4 SOLUTION The graph of y = –4 is the horizontal line that passes through the point (0, –4). Notice that every point on the line has a y-coordinate of y = –4.

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