Question

7b members pay a one - time $10 sign - up fee but only have to pay $2 per class. write an equation in the form $y = mx + b$ to represent the monthly cost, $y$, as a function of the number of classes. $y = 2x + 10$ 5 nice work! 7c sketch the two lines representing these equations on the graph below.

Explanation:

Step1: Recall the slope-intercept form

The equation \( y = mx + b \) has \( m \) as slope and \( b \) as y - intercept. For \( y = 2x+10 \), slope \( m = 2 \) (rise over run, 2 units up for 1 unit right) and y - intercept \( b = 10 \) (the line crosses y - axis at \( (0,10) \)).

Step2: Plot the y - intercept

Start by marking the point \( (0,10) \) on the y - axis.

Step3: Use the slope to find another point

From \( (0,10) \), using slope \( m = 2=\frac{2}{1} \), move 1 unit to the right (increase x by 1) and 2 units up (increase y by 2). So we get the point \( (1,12) \).

Step4: Draw the line

Connect the points \( (0,10) \) and \( (1,12) \) (and extend) to sketch the line for \( y = 2x + 10 \). For the other line (assuming there was a previous equation, but since the graph shows two lines, we follow the same process for the other equation, likely with a different slope or y - intercept, but the key is to use slope - intercept form to plot points and draw the line).

Answer:

To sketch \( y = 2x + 10 \): Plot \( (0,10) \), then use slope \( 2 \) to find \( (1,12) \), draw the line through these points. For the other line, use its equation's slope and y - intercept to plot points and draw (process similar to above). The graph should have two lines, one with y - intercept 10 and slope 2, and the other with its respective slope and y - intercept as per its equation.