Questions: Consider the following linear equation. f(x)=7x-3 Find the y-intercept of the line represented by the linear equation. Write your answer as a coordinate pair.

Solution Steps

To find the \( y \)-intercept of a linear equation in the form \( f(x) = mx + b \), we need to determine the value of \( f(x) \) when \( x = 0 \). The \( y \)-intercept is the point where the line crosses the \( y \)-axis, which occurs when \( x = 0 \). Therefore, substitute \( x = 0 \) into the equation to find the \( y \)-intercept.

The given linear equation is \( f(x) = 7x - 3 \). This equation is in the slope-intercept form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.

To find the \( y \)-intercept, we set \( x = 0 \) in the equation. Substituting \( x = 0 \) into the equation gives: \[ f(0) = 7(0) - 3 = -3 \] Thus, the \( y \)-intercept is the point where the line crosses the \( y \)-axis, which is at the coordinate pair \( (0, -3) \).

Final Answer