Questions: Find the y-intercept and the slope of the line.
4x + 2y = 6
Transcript text: Find the $y$-intercept and the slope of the line.
\[
4 x+2 y=6
\]
Solution
Solution Steps
Step 1: Finding the $y$-intercept
To find the $y$-intercept of the line given by the equation $4x + 2y = 6$, we set $x = 0$ and solve for $y$.
Substituting $x = 0$ into the equation gives $2y = 6$. Solving for $y$ yields $y = \frac{6}{2} = 3$.
Thus, the $y$-intercept of the line is at $(0, 3)$.
Step 2: Finding the slope
The slope of the line can be found by rearranging the equation into the form $y = mx + b$, where $m$ is the slope.
Starting with $4x + 2y = 6$, we isolate $y$ to get $y = -\frac{4}{2}x + \frac{6}{2}$.
Therefore, the slope $m = -\frac{4}{2} = -2$.
Final Answer:
The line given by the equation $4x + 2y = 6$ has a slope of -2 and a $y$-intercept of $(0, 3)$.