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?
$y - 1 = 4(x - 7)$
$y - 7 = 3(x - 1)$
$y - 7 = 4(x - 1)$
$y - 1 = 3(x - 7)$

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.

Step2: Determine slope and point from \(f(x)=4x + 3\)

For the linear function \(f(x)=4x+3\), the slope \(m\) of the line is \(4\) (since the equation is in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept). We know that the line passes through the point \((1,7)\) (given in the problem).

Step3: Substitute into point - slope form

Using the point - slope form \(y - y_1=m(x - x_1)\) with \(x_1 = 1\), \(y_1=7\) and \(m = 4\), we substitute these values into the formula.
Substituting \(x_1 = 1\), \(y_1 = 7\) and \(m=4\) into \(y - y_1=m(x - x_1)\), we get \(y - 7=4(x - 1)\).

Answer:

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