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Equation of Lines: Blue & Red with Coordinates

Learn to write equations for lines based on given coordinates, solve for missing coefficients in standard form equations, and practice finding equations of horizontal and vertical lines passing through points.

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Equation of Lines: Blue & Red with Coordinates

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  1. Write an equation of the specified line. a. b. Blue line Red line a. The y-coordinate of the given point on the blue line is –4. This means that all points on the line have a y-coordinate of –4. An equation of the line is y=–4. The x-coordinate of the given point on the red line is 4. This means that all points on the line have an x-coordinate of 4. An equation of the line is x= 4. b. EXAMPLE 3 Write an equation of a line SOLUTION

  2. Find the missing coefficient in the equation of the line shown. Write the completed equation. Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 EXAMPLE 4 SOLUTION STEP1 Find the value of A. Substitute the coordinates of the given point for xandyin the equation. Solve forA. Ax + 3y = 2 Write equation. A(–1) + 3(0) = 2 Substitute –1 for x and 0 for y. Simplify. –A = 2 A = –2 Divide by –1.

  3. Complete an equation in standard form EXAMPLE 4 STEP2 Complete the equation. –2x + 3y = 2 Substitute –2 for A.

  4. y=–9, x= –8 ANSWER for Examples 3 and 4 GUIDED PRACTICE Write equations of the horizontal and vertical lines that pass through the given point. 3. (–8, –9)

  5. y=–5, x= 13 ANSWER for Examples 3 and 4 GUIDED PRACTICE Write equations of the horizontal and vertical lines that pass through the given point. 4. (13, –5)

  6. ANSWER 3; –4x + 3y = 7 Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 for Examples 3 and 4 Write an equation of a line GUIDED PRACTICE Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. 5. –4x + By = 7, (–1, 1)

  7. ANSWER –7; –7x +y = –3 Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 for Examples 3 and 4 Write an equation of a line GUIDED PRACTICE Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. 6.Ax + y = –3, (2, 11)

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