Question

The equation y = 2x + 3 represents the perimeter of an isosceles triangle with two equal sides that are x inches in length. The third side is a constant 3 inches. Graph this equation. What is the subject of this question?

Answer 1

The graph of the equation
`\( y = 2x + 3 \)` represents the perimeter of an isosceles triangle, where two equal sides are
`\( x \)` inches each, and the third side is a constant 3 inches.

Step-by-step explanation:

The given equation
`\( y = 2x + 3 \)` is a linear equation in slope-intercept form
`(\( y = mx + b \))`, where
`\( m \)` represents the slope and
`\( b \)` is the y-intercept. In this context,
`\( x \)` represents the length of one of the equal sides of an isosceles triangle, and
`\( y \)` represents the perimeter of the triangle. The coefficient of
`\( x \)` is 2, indicating that the length of the other equal side is also
`\( x \)` . The constant term 3 represents the length of the third side of the isosceles triangle.

To graph this equation, one can choose values for
`\( x \)`, calculate the corresponding
`\( y \)` values using the equation, and plot the points on a coordinate plane. The resulting graph will be a straight line, as the equation is linear. The slope of the line is 2, indicating the rate at which the perimeter increases with the length of one side of the triangle.

In the context of the question, the subject is the isosceles triangle's perimeter, and the equation allows us to relate the length of one side
`(\( x \))` to the perimeter
`(\( y \))`. Therefore, the subject of the question is the relationship between the sides and perimeter of the isosceles triangle as represented by the given equation.