Question

if you were to graph a line with a slope of \\(\frac{3}{2}\\) that intercepts the y-axis at -2 on the coordinate plane, one point on that line would have a y coordinate of 4 with an x coordinate of what number?

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the slope $m=\frac{3}{2}$ and the y - intercept $b=- 2$ (since the line intercepts the y - axis at $y=-2$). So the equation of the line is $y=\frac{3}{2}x-2$.

Step2: Substitute $x = 4$ into the equation

We want to find the $y$ - coordinate when $x = 4$. Substitute $x = 4$ into $y=\frac{3}{2}x-2$.
First, calculate $\frac{3}{2}\times4$. $\frac{3}{2}\times4=\frac{3\times4}{2}=3\times2 = 6$.
Then, $y=6 - 2$.

Step3: Calculate the value of $y$

$y=6 - 2=4$.

Answer:

4