Write an equation that relates the quantities. The monthly...

Write an equation that relates the quantities. The monthly payment $p$ on a mortgage varies directly with the amount borrowed $B$. If the monthly payment on a 30 -year mortgage is $\$ 6.49$ for every $\$ 1000$ borrowed, find a linear equation that relates the monthly payment $p$ to the amount borrowed $B$ for a mortgage with these terms. Then find the monthly payment $p$ when the amount borrowed $B$ is $\$ 145,000$.

Write an equation that relates the quantities.
The monthly payment $p$ on a mortgage varies directly with the amount borrowed $B$. If the monthly payment on a 30 -year mortgage is $\$ 6.49$ for every $\$ 1000$ borrowed, find a linear equation that relates the monthly payment $p$ to the amount borrowed $B$ for a mortgage with these terms. Then find the monthly payment $p$ when the amount borrowed $B$ is $\$ 145,000$.

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Key Concepts

Direct Variation

Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. This means that as one variable increases or decreases, the other variable changes proportionally. In mathematical terms, this relationship is often written as y = kx, where k is the constant of proportionality.

Constant of Proportionality

The constant of proportionality is the factor that relates the two variables in a direct variation. It represents the rate at which one variable changes with respect to the other. In an equation like y = kx, k is this constant and determines the steepness or rate of the linear relationship.

Linear Equation

A linear equation is an equation that form a straight line when graphed. It typically has the form y = mx + b, where m is the slope and b is the y-intercept. In the case of direct variation, the relationship simplifies to y = kx since the y-intercept is zero, emphasizing the proportional relationship between the variables.

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