Write the equation in point slope form given (2,5) and is parallel to y = 3x + 8

Bavikhove8h
2022-09-05
Answered

Write the equation in point slope form given (2,5) and is parallel to y = 3x + 8

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Adelaide Kemp

Answered 2022-09-06
Author has **10** answers

Parallal lines have equal slope. The slope of the line y=3x+8 is 3[y=mx+c]. Therefore the slope of the line is also 3.

The equation of line passing through (2,5) is $y-{y}_{1}=m(x-{x}_{1})\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y-5=3(x-2)\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y-5=3x-6\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y=3x-6+5\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y=3x-1$

The equation of line passing through (2,5) is $y-{y}_{1}=m(x-{x}_{1})\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y-5=3(x-2)\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y-5=3x-6\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y=3x-6+5\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y=3x-1$

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Question: Given a system of linear equations

$a{x}_{1}+a{x}_{2}+a{x}_{3}=2\phantom{\rule{0ex}{0ex}}{x}_{1}+a{x}_{2}+a{x}_{3}=0\phantom{\rule{0ex}{0ex}}2{x}_{1}+3{x}_{2}+a{x}_{3}=1$

For what 2 values of $a$ will the system's augmented matrix have less than 3 pivots?

I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding $a$?

$a{x}_{1}+a{x}_{2}+a{x}_{3}=2\phantom{\rule{0ex}{0ex}}{x}_{1}+a{x}_{2}+a{x}_{3}=0\phantom{\rule{0ex}{0ex}}2{x}_{1}+3{x}_{2}+a{x}_{3}=1$

For what 2 values of $a$ will the system's augmented matrix have less than 3 pivots?

I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding $a$?