Bentley Floyd

2023-03-09

How to write an equation of a line with slope of 3 and contains the point (4, 9)?

angel52594672ve

Beginner2023-03-10Added 3 answers

$\text{the equation of a line in}\phantom{\rule{1ex}{0ex}}{\text{slope-intercept form}}$ is.

$\u2022{x}y=mx+b$

$\text{where m is the slope and b the y-intercept}$

$\text{here}\phantom{\rule{1ex}{0ex}}m=3$

$\Rightarrow y=3x+b\leftarrow {\text{is the partial equation}}$

$\text{to find b substitute}\phantom{\rule{1ex}{0ex}}(4,9)\phantom{\rule{1ex}{0ex}}\text{into the partial equation}$

$9=12+b\Rightarrow b=9-12=-3$

$\Rightarrow y=3x-3\leftarrow {\text{is the equation of the line}}$

$\u2022{x}y=mx+b$

$\text{where m is the slope and b the y-intercept}$

$\text{here}\phantom{\rule{1ex}{0ex}}m=3$

$\Rightarrow y=3x+b\leftarrow {\text{is the partial equation}}$

$\text{to find b substitute}\phantom{\rule{1ex}{0ex}}(4,9)\phantom{\rule{1ex}{0ex}}\text{into the partial equation}$

$9=12+b\Rightarrow b=9-12=-3$

$\Rightarrow y=3x-3\leftarrow {\text{is the equation of the line}}$

polemann7tm

Beginner2023-03-11Added 4 answers

The equation of a line in point-slope form is as follows:

$y-{y}_{1}=m(x-{x}_{1})$

Make the following substitutions:

${x}_{1}=4$ (the x-coordinate of the point)

${y}_{1}=9$ (the y-coordinate of the same point)

$m=3$ (the slope of the line)

You will then have:

$y-9=3(x-4)$

Then simplify:

$y-9=3(x-4)$

$y-9=3x-12$

$y=3x-3$

$y-{y}_{1}=m(x-{x}_{1})$

Make the following substitutions:

${x}_{1}=4$ (the x-coordinate of the point)

${y}_{1}=9$ (the y-coordinate of the same point)

$m=3$ (the slope of the line)

You will then have:

$y-9=3(x-4)$

Then simplify:

$y-9=3(x-4)$

$y-9=3x-12$

$y=3x-3$