Question

look at this graph:
what is the equation of the line in point - slope form?

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-7, 0)\) and \((-5, 10)\) (assuming the red point is \((-5, 10)\) and the x-intercept is \((-7, 0)\)).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-7,0)\) and \((x_2,y_2)=(-5,10)\). Then \(m=\frac{10 - 0}{-5 - (-7)}=\frac{10}{2} = 5\).

Step3: Use point - slope form formula

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((-7,0)\) and \(m = 5\). Substituting these values into the formula, we get \(y-0 = 5(x - (-7))\), which simplifies to \(y=5(x + 7)\). We could also use the other point \((-5,10)\). Using \((x_1,y_1)=(-5,10)\) and \(m = 5\), we have \(y - 10=5(x+5)\).

Answer:

\(y - 10 = 5(x + 5)\) (or \(y=5(x + 7)\))