There are several formulas for the equation of a line 1) Point slope of a line Use this when given slope m and a point on the line. Use this when given two points on a line by finding m first. 2) Slope intercept from a line (y-intercept) y=mx+b Use this when given slope m and y-intercept 3) General form of a line Ax+By+C=0 The graph is always a line. 4) Special lines Equation : y=b Equation: x=a EXAMPLE 1 Find the slope of the line whose equation is 3x+2y=6 Solve the equation for y=mx+b because m is the slope. EXAMPLE 2 Write the equation of the line through (-2,4) and (-9,2). Find the slope Use the point slope form of a line (you can use either point) You can use fraction or avoid fraction. OR These two answers are equivalent EXAMPLE 3 Find the equation of line through (1,-2) and perpendicular to 3x+2y=6 Find the slope of the given line by solving for y 2y=-3x+6 y=-3/2x+3 slope=-3/2 The slope of the perpendicular to the given line has a slope equal to -(1/(-3/2)) = 2/3 Now we use point slope formula
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