Question

I need help immediately

Answer 1

`\textsf{Carlos:} \quad y=(5)/(7)x`

`\textsf{Carlita:} \quad y=(7)/(5)x`

Explanation:

To find the equation of a line from its graph:

• Identify the point the line crosses the y-axis (the y-intercept) and another point on the graph.
• Substitute the two points into the slope formula and calculate the slope of the line.
• Substitute the slope and y-intercept into the slope-intercept form of a linear equation.

Carlos's graph

From inspection of the given graph:

• y-intercept: (x₁, y₁) = (0, 0)
• point on the line: (x₂, y₂) = (7, 5)

Calculate the slope:

`\textsf{Slope}\;(m)=(y_2-y_1)/(x_2-x_1)=(5-0)/(7-0)=(5)/(7)`

Substitute the slope (m) and y-intercept (b) into the slope-intercept form of a linear equation:

`y=mx+b`

`y=(5)/(7)x+0`

`y=(5)/(7)x`

Therefore, the equation of Carlos's graph is:

`\large\boxed{\boxed{y=(5)/(7)x}}`

The x-axis of this graph is labelled "Pounds", and the y-axis is labelled "Dollars". Therefore, the graph likely shows how the cost changes as the weight varies. The question that could be best answered using Carlos's graph is about the price for a certain weight in pounds, or how price changes with weight.

Carlita's graph

From inspection of the given graph:

• y-intercept: (x₁, y₁) = (0, 0)
• point on the line: (x₂, y₂) = (5, 7)

Calculate the slope:

`\textsf{Slope}\;(m)=(y_2-y_1)/(x_2-x_1)=(7-0)/(5-0)=(7)/(5)`

Substitute the slope (m) and y-intercept (b) into the slope-intercept form of a linear equation:

`y=mx+b`

`y=(7)/(5)x+0`

`y=(7)/(5)x`

Therefore, the equation of Carlita's graph is:

`\large\boxed{\boxed{y=(7)/(5)x}}`

The x-axis of this graph is labelled "Dollars", and the y-axis is labelled "Pounds". Therefore, the graph likely shows how the weight changes as the cost varies. The question that could be best answered using Carlita's graph is about the weight for a certain cost in dollars, or how weight changes with cost.