3.5 Write and Graph Equations of Lines

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Presentation transcript:

3.5 Write and Graph Equations of Lines

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

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

EXAMPLE 5 Graph a line with equation in standard form Graph 3x + 4y = 12. SOLUTION The equation is in standard form, so you can use the intercepts. STEP 1 Find the intercepts. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. 3x +4y = 12 3x +4y = 12 3x +4 ( 0 ) = 12 3 ( 0 ) + 4y = 12 x = 4 y = 3

EXAMPLE 5 Graph a line with equation in standard form STEP 2 Graph the line. The intercepts are (4, 0) and (0, 3). Graph these points, then draw a line through the points.

GUIDED PRACTICE for Examples 4 and 5 Graph the equation 2x – 3y = 6 SOLUTION

GUIDED PRACTICE for Examples 4 and 5 Graph the equation y = 4 SOLUTION

Write an equation of the line through point (2,3) with a slope of 5. y = mx + b 3 = 5(2) + b -7 = b y = 5x - 7

y = 5x - 7 y = mx + b 6 = 5(5) + b -19 = b y = 5x - 19 Write an equation for a line parallel to this line and passing through point (5,6) y = mx + b 6 = 5(5) + b -19 = b y = 5x - 19