Tyreek is saving money to buy a new video game system. He starts with $10.75 and saves $15.50 per week.

Question

Write the equation of the line in slope-intercept form that represents Tyreek's savings, y, in terms of weeks, x
The equation in slope-intercept form is y= (____) x + (___)

Answer 1

To write the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:

1. Identify the Starting Amount (y-intercept, \( b \)): Tyreek starts with $10.75, so \( b = 10.75 \).

2. Identify the Rate of Savings (slope, \( m \)): Tyreek saves $15.50 per week, so \( m = 15.50 \).

Combining this information, the equation of the line that represents Tyreek's savings in terms of weeks is:

\[ y = 15.50x + 10.75 \]

So, the equation in slope-intercept form is:

\[ y = (15.50)x + (10.75) \]

Answer 2

Write the equation of the line in slope-intercept form that passes through the points (0,2.3)
, (5,−1.9)
.(1 point)
The equation in slope-intercept form is (___)= ( __)x +(____)

Answer 3

To find the equation of the line in slope-intercept form \( y = mx + b \) that passes through the points \( (0, 2.3) \) and \( (5, -1.9) \), we first need to calculate the slope \( m \) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can assign:

• \( (x_1, y_1) = (0, 2.3) \)
• \( (x_2, y_2) = (5, -1.9) \)

Now, substituting the values:

\[ m = \frac{-1.9 - 2.3}{5 - 0} = \frac{-4.2}{5} = -0.84 \]

Now that we have the slope \( m = -0.84 \), we can use the y-intercept \( b \) from the first point \( (0, 2.3) \), which gives \( b = 2.3 \).

Now, we can write the equation in slope-intercept form:

\[ y = -0.84x + 2.3 \]

Thus, the equation in slope-intercept form is:

\[ y = (-0.84)x + (2.3) \]