Bentley Floyd

2023-03-09

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

angel52594672ve

$\text{the equation of a line in}\phantom{\rule{1ex}{0ex}}\text{slope-intercept form}$ is.
$•xy=mx+b$
$\text{where m is the slope and b the y-intercept}$
$\text{here}\phantom{\rule{1ex}{0ex}}m=3$
$⇒y=3x+b←\text{is the partial equation}$
$\text{to find b substitute}\phantom{\rule{1ex}{0ex}}\left(4,9\right)\phantom{\rule{1ex}{0ex}}\text{into the partial equation}$
$9=12+b⇒b=9-12=-3$
$⇒y=3x-3←\text{is the equation of the line}$

polemann7tm

The equation of a line in point-slope form is as follows:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
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:
$y-9=3\left(x-4\right)$
Then simplify:
$y-9=3\left(x-4\right)$
$y-9=3x-12$
$y=3x-3$

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