Question

1. a table of values is shown below.

x	45	60	75
y	8	9	10

which equation describes the linear relationship shown in the table of values?
a. $y = \frac{1}{15}x + 5$
b. $y = \frac{1}{15}x + 8$
c. $y = 15x + 5$
d. $y = 15x + 8$

1. a graph of a linear equation is shown below.

which equation describes the graph?
graph of a line on a coordinate plane with x-axis from -8 to 8 and y-axis from -8 to 8, passing through points, with options a. $y = \frac{1}{2}x - 1.5$, b. $y = \frac{1}{2}x + 3$, c. $y = 2x - 1.5$ (partial options shown)

Explanation:

Question 1

Step 1: Find the slope (m)

The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((45, 8)\) and \((60, 9)\):
\( m=\frac{9 - 8}{60 - 45}=\frac{1}{15} \)

Step 2: Find the y - intercept (b)

Use the slope - intercept form \( y = mx + b \) and the point \((45, 8)\) with \( m=\frac{1}{15} \):
\( 8=\frac{1}{15}(45)+b \)
\( 8 = 3 + b \)
Subtract 3 from both sides: \( b = 8 - 3=5 \)
So the equation is \( y=\frac{1}{15}x + 5 \)

Step 1: Find the slope (m)

The graph passes through \((0, 3)\) (y - intercept) and let's take another point, say \((2, 4)\). The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \)
\( m=\frac{4 - 3}{2 - 0}=\frac{1}{2} \)

Step 2: Find the y - intercept (b)

From the graph, when \( x = 0 \), \( y = 3 \), so \( b = 3 \)
The equation of the line in slope - intercept form \( y=mx + b \) is \( y=\frac{1}{2}x+3 \)

Answer:

A. \( y=\frac{1}{15}x + 5 \)

Question 2