Question

chin was shown the graph of a line that contained point (1, 7). he wrote $f(x) = 4x + 3$ to correctly represent the line. which of these equations could represent the same line?
$\circ\\ y - 7 = 3(x - 1)$
$\circ\\ y - 1 = 3(x - 7)$
$\circ\\ y - 7 = 4(x - 1)$
$\circ\\ y - 1 = 4(x - 7)$

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.

First, we know that the equation of the line is $f(x)=4x + 3$, so the slope $m$ of the line is $4$. Also, the line contains the point $(1,7)$, so $x_1 = 1$ and $y_1=7$.

Step2: Substitute into point - slope form

Substituting $m = 4$, $x_1=1$ and $y_1 = 7$ into the point - slope form $y - y_1=m(x - x_1)$, we get:

$y-7 = 4(x - 1)$

Answer:

$y - 7=4(x - 1)$ (the third option)