Question

line equations from point/slope
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question
what is the equation of the line that passes through the point (2,8) and has a slope of \\(\frac{3}{2}\\)?
answer
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Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 2$, $y_1=8$ and $m=\frac{3}{2}$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 2$, $y_1 = 8$ and $m=\frac{3}{2}$ into the point - slope formula:
$y - 8=\frac{3}{2}(x - 2)$

Step3: Simplify the equation

First, distribute $\frac{3}{2}$ on the right - hand side:
$y - 8=\frac{3}{2}x-3$
Then, add 8 to both sides of the equation to solve for $y$:
$y=\frac{3}{2}x-3 + 8$
$y=\frac{3}{2}x+5$

Answer:

$y = \frac{3}{2}x + 5$