Question

enter the correct answers that completes the sentence below. the graph of the line $y - 5 = 4(x - 4)$ has a slope of $\square$ and passes through the point $(4, \square)$.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line 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 that the line passes through.

Step2: Identify slope and point

For the equation \(y - 5=4(x - 4)\), comparing it with the point - slope form \(y - y_1=m(x - x_1)\), we can see that \(m = 4\) (the slope) and \(x_1 = 4\), \(y_1=5\). So the line passes through the point \((4,5)\).

Answer:

The slope is \(4\) and the \(y\) - coordinate of the point \((4,\square)\) is \(5\). So the answers are \(4\) and \(5\) (in the first box: \(4\), in the second box: \(5\)).