Question

m3|l2 graphs of proportional relationships one way to figure this out is to find an equation for each graph. let’s start with graph 1. what’s the equation for graph 1? use x to represent the time in hours, and use y to represent the rainfall in inches. graph 1 graph of a line with a point at (lets infer from the grid, maybe x corresponding to the x - axis (time) and y - axis (rainfall) with a point at, say, when x is some value, y is 0.8). there are buttons: 0.2, =, x, +, 0.4, ·, y, and a more button.

Explanation:

Step1: Identify the type of relationship

The graph represents a proportional relationship (since it's a straight line through the origin, or we can check the slope). For a proportional relationship, the equation is of the form \( y = kx \), where \( k \) is the constant of proportionality (slope).

Step2: Find two points on the graph

Looking at the graph, we can see a point at (let's assume the x - axis is time in hours and y - axis is rainfall in inches). From the grid, let's find the coordinates of the marked point. The marked point seems to be at \( x = 2 \) (since from the origin, moving 2 units along x - axis) and \( y = 0.8 \) (moving 0.8 units along y - axis). Wait, let's check the grid. Wait, maybe the x - axis has each grid as 1 unit? Wait, no, maybe the x - value for the marked point: let's see, the y - value is 0.8, and let's find the slope. Alternatively, let's take two points. Let's assume when \( x = 0 \), \( y = 0 \) (since it's a proportional graph, passes through origin). Then the marked point: let's see the coordinates. If we look at the graph, the blue dot is at \( x = 2 \) (since from the origin, x = 2, y = 0.8). So slope \( k=\frac{y}{x}=\frac{0.8}{2}=0.4 \). Wait, no, wait, maybe the x - axis is 1 unit per grid. Wait, another way: the equation for proportional relationship is \( y = mx \), where m is slope. Let's take the point (x, y) from the graph. Let's say when x = 2, y = 0.8. Then \( m=\frac{y}{x}=\frac{0.8}{2}=0.4 \). Wait, but let's check with another point. If x = 1, then y should be 0.4. Let's see the graph: when x = 1, y is 0.4? Wait, the y - axis has 0.2, 0.4, 0.6, 0.8, 1.0. So if x = 2, y = 0.8, then the slope is \( \frac{0.8}{2}=0.4 \). So the equation is \( y = 0.4x \). Wait, but let's check the given numbers. The options are 0.2, =, x, +, 0.4, ·, y. Wait, the equation should be \( y = 0.4x \). Let's verify: if x = 2, then y = 0.4*2 = 0.8, which matches the marked point. So the equation is \( y = 0.4x \).

Answer:

\( y = 0.4x \) (or using the given buttons: we can form \( y = 0.4 \cdot x \))