Question

peyton steers a remote - control car. the equation $y = 3x + 4$ can be used to find $y$, the car’s distance from peyton in feet, after $x$ seconds. the $y$-intercept is 4. it tells you the car starts 4 feet from peyton. plot the $y$-intercept on the graph.

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a linear equation \(y = mx + b\) is the value of \(y\) when \(x = 0\). For the equation \(y=3x + 4\), when \(x = 0\), \(y=4\). So the y - intercept is at the point \((0,4)\).

Step2: Locate (0,4) on the graph

On the given graph, the x - axis represents time (in seconds) and the y - axis represents distance (in feet). The point \((0,4)\) is at the origin of the x - axis (x = 0) and at \(y = 4\) on the y - axis. So we plot the point where \(x = 0\) and \(y = 4\) (the intersection of the vertical line through \(x = 0\) and the horizontal line through \(y = 4\)).

Answer:

To plot the y - intercept, we mark the point \((0,4)\) on the graph. This point is on the y - axis (since \(x = 0\)) and at a distance of 4 feet (since \(y = 4\)) from Peyton at time \(x = 0\) seconds.