Question

4.
equation: $y - 5 = 3x$
slope: ____ point: _____

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is given by $y - y_1=m(x - x_1)$, where $m$ is the slope of the line and $(x_1,y_1)$ is a point on the line.

Step2: Compare with given equation

The given equation is $y - 5=3x$. We can rewrite the right - hand side as $3(x - 0)$ (since $3x=3(x - 0)$). So, comparing $y - 5 = 3(x - 0)$ with the point - slope form $y - y_1=m(x - x_1)$:

• For the slope $m$: By comparing, we see that $m = 3$.
• For the point $(x_1,y_1)$: By comparing, we see that $x_1 = 0$ and $y_1=5$, so the point is $(0,5)$.

Answer:

Slope: $3$; Point: $(0,5)$