cora says she doesn't need to know the y-intercept of a line to write its equation, just its slope and some other point on the line. Is she correct? Explain. If Cora is correct, explain how to find the equation of a line with a alope of -1/3 that includes the point (2,6).
Accepted Solution
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Answer:The equation of line with given slope that include given points is 3 y + x - 20 = 0Step-by-step explanation:According to Cora , if we know the slope and points on a line then we can write the equation of a line . Since , The equation of line in slope-intercept form is y = m x + cWhere m is the slope of line , and if we know the points ( x , y ) which satisfy the line then constant term c can be get and the equation of line can be formed .So , From the statement said above it is clear that she is correct .Now , Again Given as :Slope of a line is m = - [tex]\frac{1}{3}[/tex]That include points ( 2 , 6 )Now from the equation of line as y = m x + c∴ 6 = - [tex]\frac{1}{3}[/tex] ( 2 ) + cOr, 6 = - [tex]\frac{2}{3}[/tex] + cSo , c = 6 + [tex]\frac{2}{3}[/tex] or, c = [tex]\frac{18 + 2}{3}[/tex] ∴ c = [tex]\frac{20}{3}[/tex] So, The equation of line can be written as y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{20}{3}[/tex] Or, 3 y = - x + 20I.e 3 y + x - 20 = 0Hence The equation of line with given slope that include given points is 3 y + x - 20 = 0 Answer