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25.06.2019 •
Mathematics
Can someone me with part b question zoom into the picture if it’s unreadable. ( for the ! )
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Ответ:
x + 3y = 2
Step-by-step explanation:The line: y-3 = 3(x+1) or y = 3x+4
You may (1) first find the equation of the perpendicular line that passes thru (5,-1), then convert it to Standard Form or (2) convert the equation to Standard Form, then find the equation of the line that passes thru (5,-1). See if you can follow both methods:
Important: If a line has slope m, then all perpendicular lines have a slope of (-1/m). That's called the negative reciprocal.
(1) find the equation in slope-intercept form, then convert to Standard Form
The line: y-3 = 3(x+1) or y = 3x+4
Perpendicular line: y = (-1/3)x + b [and we need point (5,-1) to find b
-1 = (-1/3)(5) + b
-1 = -5/3 + b
2/3 = b
The perpendicular line is: y = (-1/3)x + 2/3
The Standard Form of the equation of a line looks like: Ax+By=C
The perpendicular line is:
(1/3)x + y = 2/3
x + 3y = 2 [by convention, coefficient of x is positive; x is first;
get rid of fractions]
(2) Convert to Standard Form, then find the specific equation
The line: y-3 = 3(x+1) or y = 3x+4
In Standard Form: 3x - y = 4 [Note: slope is (-A/B) = (-3)/(-1) = 3
Slope of all parallel lines: (-1/3) [that is, -A/B]
Equation of parallel line: x + 3y = D [and we need point (5,-1) to determine D]
5 + 3(-1) = D
2 = D
The parallel line, in Standard Form, is : x + 3y = 2