Question 1
Find the equation of the line that passes through the point $(-3,7)$ and has slope $\frac{2}{3}$. Simplify your equation to the following form.
\[
y=\frac{2}{3} x+
\]
What is the missing value in the equation above?
Answer
So, the missing value in the equation \(y = \frac{2}{3}x + b\) is \(\boxed{9}\).
Step 1 ：We are given a point (-3,7) and a slope of 2/3. We are asked to find the equation of the line that passes through this point and has this slope.
Step 2 ：We can use the point-slope form of a line, which is \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is the given point.
Step 3 ：Substituting the given values into the equation, we get \(y - 7 = \frac{2}{3}(x + 3)\).
Step 4 ：Solving for \(y\), we get \(y = \frac{2}{3}x + 9\).
Step 5 ：So, the missing value in the equation \(y = \frac{2}{3}x + b\) is \(\boxed{9}\).
