Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
2 answers:
Answer:
(a). <em>y = 3x - 11 ;</em> (b). <em>y = </em><em> x - 1 </em>
Step-by-step explanation:
Parallel lines have the same slopes
Slopes of perpendicular lines are opposite reciprocals.
(3, - 2)
The slope of given line is 3
<em>(a)</em>. Equation of ║ line is
y + 2 = 3(x - 3)
<em>y = 3x - 11</em>
<em>(b).</em> Slope of perpendicular line is
y + 2 = (x - 3)
<em>y = </em><em> x - 1</em>
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Answer:
(3, -3 8/9)
Step-by-step explanation:
Use a slope calculation or a graph to find the slope of the line.
m = (y-y)/(x-x)
m = (-3- -5)/(7- -2)
m = 2/9
Then write the equation of the line. I used point-slope form. (You could use y=mx+b, slope-intercept form, but you'd have to first calculate b as well)
Point-slope form:
y -Y = m(x-X)
y - -3 = 2/9(x- 7)
y + 3 = 2/9(x - 7)
We know the x-coordinate of the point we're looking for is 3. Fill that in as well and calculate the y that goes with it.
y + 3 = 2/9(3-7)
y+3=2/9(-4)
y = -8/9 - 3
y = -3 8/9
In decimal form this is -3.8888repeating
see image.
The point at x=3 on the line between M(7,-3) and N(-2,-5) is (3, -3 8/9).
