Question

the equation of a linear function in point - slope form is $y - y_1 = m(x - x_1)$. harold correctly wrote the equation $y = 3(x - 7)$ using a point and the slope. which point did harold use?
$(0, 7)$
$(7, 3)$
$(3, 7)$
$(7, 0)$

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. We can rewrite the given equation \(y = 3(x - 7)\) in the form \(y-0=3(x - 7)\) (by subtracting 0 from the left - hand side and recognizing that \(y-0 = y\)).

Step2: Identify the point

Comparing \(y-0=3(x - 7)\) with the point - slope form \(y - y_1=m(x - x_1)\), we can see that \(x_1 = 7\) and \(y_1=0\). So the point \((x_1,y_1)\) is \((7,0)\).

Answer:

\((7,0)\)