Question

score: 6/10 penalty: 0.5 off question what is the equation of the line that passes through the point (4, 6) and has a slope of \\(\frac{3}{2}\\)? answer attempt 1 out of 2

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation 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, $x_1 = 4$, $y_1=6$ and $m=\frac{3}{2}$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 4$, $y_1 = 6$ and $m=\frac{3}{2}$ into the point - slope form:
$y - 6=\frac{3}{2}(x - 4)$

Step3: Simplify the equation

First, distribute $\frac{3}{2}$ on the right - hand side:
$y - 6=\frac{3}{2}x-6$
Then, add 6 to both sides of the equation:
$y=\frac{3}{2}x-6 + 6$
$y=\frac{3}{2}x$

Answer:

$y=\frac{3}{2}x$ (or in standard form $3x - 2y = 0$, but the slope - intercept form is more straightforward here)