Question

since the beginning of this year, seikis band has learned 4 new songs each month. it is 1 month into the year and they now know how to play 10 songs. determine the equation, in slope-intercept form, of the line that represents the total number of songs the band can play x months after the beginning of this year. y =

Explanation:

Step1: Start with point - slope form

We are given the point - slope form of the line as \(y - 10=4(x - 1)\). The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \(m\) is the slope and \((x_1,y_1)\) is a point on the line. Here, \(m = 4\) and \((x_1,y_1)=(1,10)\).

Step2: Expand the right - hand side

First, we expand \(4(x - 1)\) using the distributive property \(a(b - c)=ab - ac\). So, \(4(x - 1)=4x-4\). The equation becomes \(y - 10 = 4x-4\).

Step3: Solve for y (slope - intercept form)

To get the slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), we add 10 to both sides of the equation \(y - 10 = 4x-4\).
\(y=4x-4 + 10\)
Simplify the right - hand side: \(-4 + 10 = 6\). So, \(y = 4x+6\).

Answer:

\(y = 4x + 6\)