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?
○ y - 7 = 3(x - 1)
○ y - 1 = 3(x - 7)
○ y - 7 = 4(x - 1)
○ 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.
We know that the function $f(x)=4x + 3$ is in slope - intercept form ($y=mx + b$), where the slope $m = 4$. The line also contains the point $(1,7)$, so $x_1 = 1$ and $y_1=7$.

Step2: Substitute into Point - Slope Form

Substitute $m = 4$, $x_1=1$ 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)