Question

can write equations from graphs of proportional relationships.

write equation of the line

write equation of the line

write an equation of the line:

a point (6,9) is labeled above. which statement about the graph is true?

a) the unit rate is 6 games per dollar
b) the unit rate is $9.00 per game
c) the unit rate is $1.50 per game
d) the unit rate is 1.5 games per dollar

Explanation:

Top - Left Graph:

Step1: Identify the point

The line passes through \((2, 7)\) and the origin \((0,0)\)? Wait, no, looking at the graph, when \(x = 2\), \(y=7\)? Wait, no, maybe I misread. Wait, the line starts at the origin and goes to \((2,7)\)? Wait, no, the graph has a line from \((0,0)\) to \((2,7)\)? Wait, no, the y - axis has marks. Wait, maybe the point is \((2,7)\). So the slope \(m=\frac{y}{x}\) for a proportional relationship (since it passes through the origin, \(y = mx\)). So \(m=\frac{7}{2}=3.5\)? Wait, no, maybe the graph is different. Wait, maybe the line goes through \((2,7)\), so the equation is \(y=\frac{7}{2}x\) or \(y = 3.5x\). Wait, maybe I made a mistake. Wait, the x - axis is up to 10, y - axis up to 10? No, the top - left graph: when \(x = 2\), \(y = 7\)? Wait, maybe the correct point is \((2,7)\), so the slope \(m=\frac{7}{2}=3.5\), so the equation is \(y = 3.5x\) or \(y=\frac{7}{2}x\).

Step2: Write the equation

Since it's a proportional relationship (passes through the origin), \(y=mx\), where \(m=\frac{y}{x}\). If \(x = 2\), \(y = 7\), then \(m=\frac{7}{2}\), so \(y=\frac{7}{2}x\) or \(y = 3.5x\).

Top - Right Graph:

Step1: Identify a point

Looking at the graph, there is a point, say, when \(x = 18\), \(y = 32\)? Wait, no, maybe the point is \((18,32)\)? Wait, no, the y - axis has marks. Wait, the line passes through the origin. Let's assume a point \((x,y)\). Let's say when \(x = 18\), \(y = 32\)? No, maybe the slope is \(\frac{y}{x}\). Wait, maybe the graph has a point \((18,32)\)? No, maybe I misread. Wait, the x - axis is up to 30, y - axis up to 50. Let's take a point, say, if \(x = 18\), \(y = 32\), then \(m=\frac{32}{18}=\frac{16}{9}\approx1.78\). But maybe the correct point is \((18,30)\)? No, this is unclear. Wait, maybe the graph is of a proportional relationship, so \(y=mx\). Let's assume a point \((x,y)\) on the line. For example, if we take the point where \(x = 18\) and \(y = 30\), then \(m=\frac{30}{18}=\frac{5}{3}\approx1.67\). But maybe the intended point is \((18,30)\), so \(y=\frac{5}{3}x\).

Bottom - Left Graph:

Step1: Identify the point

The line passes through \((9,54)\) and the origin \((0,0)\). For a proportional relationship \(y = mx\), the slope \(m=\frac{y}{x}\).

Step2: Calculate the slope

\(m=\frac{54}{9}=6\). So the equation is \(y = 6x\).

Bottom - Right Graph (Multiple - Choice Question):

Answer:

\(y = 6x\)

Bottom - Right Graph Answer: