Presentation on theme: "1.3 Linear Equations in Two Variables"— Presentation transcript:
11.3 Linear Equations in Two Variables Slope of a LineFind the slope of the lines passing through…(-2,0) and (3,1)(-1,2) and (2,2)(4,-3) and (4,5)
2Point-slope Form of the Equation of a Line Given a point (x1,y1) and slope my – y1 = m(x – x1)Ex. Find an equation of the line that passesthrough the point (1,-2) and has a slope of 3.y – (-2) = 3(x – 1)y + 2 = 3(x – 1)0 = 3x – y - 5
3Summary of Equations of Lines General Form Ax + By + C = 0Vertical Line x = aHorizontal Line y = bSlope-intercept y = mx + bPoint-slope form y – y1 = m(x – x1)Parallel lines have slopes that are Equal.Perpendicular lines have negative reciprocalslopes.
4Ex. Find the equations of the lines that pass through the point (2,-1) and are a.) parallel toand b.) perpendicular to the line 2x – 3y = 5.First, solve for y and find the slope of the line.a.) m = 2/3Use point-slope formMult. each termby 3.3y + 3 = 2x - 40 = 2x – 3y – 7 or
5b.) What is our slope?Use point-slope form to start. Then put ingeneral form.Dist.Mult. By 2