which equation represents the line with slope $\frac{7}{3}$ that passes through the point $(4, - 7)$?\na $y…

which equation represents the line with slope $\frac{7}{3}$ that passes through the point $(4, - 7)$?\na $y + 7=\frac{7}{3}(x - 4)$\nb $y - 7=\frac{7}{3}(x - 4)$\nc $y + 4=\frac{7}{3}(x + 7)$\nd $y - 4=\frac{7}{3}(x - 7)$

which equation represents the line with slope $\frac{7}{3}$ that passes through the point $(4, - 7)$?\na $y + 7=\frac{7}{3}(x - 4)$\nb $y - 7=\frac{7}{3}(x - 4)$\nc $y + 4=\frac{7}{3}(x + 7)$\nd $y - 4=\frac{7}{3}(x - 7)$

Answer

Explanation:

Step1: Recall point - slope form

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

Step2: Identify values

Given $m = \frac{7}{3}$, $x_1 = 4$, and $y_1=-7$.

Step3: Substitute values

Substitute into the point - slope form: $y-(-7)=\frac{7}{3}(x - 4)$, which simplifies to $y + 7=\frac{7}{3}(x - 4)$.

Answer:

A. $y + 7=\frac{7}{3}(x - 4)$