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)

## Step 1<br />The problem provides us with a line equation \(f(x) = 4x + 3\), which passes through the point (1,7). We are asked to find an equation that could represent the same line.<br /><br />## Step 2<br />The equation of a line in point-slope form 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.<br /><br />## Step 3<br />In the given equation \(f(x) = 4x + 3\), the slope \(m\) is 4 and the point \((x_1, y_1)\) is (1,7).<br /><br />## Step 4<br />Substituting these values into the point-slope form, we get \(y - 7 = 4(x - 1)\).<br /><br />## Step 5<br />Comparing this with the given options, we see that the equation \(y - 7 = 4(x - 1)\) matches our derived equation.