Problem 18 Graph $y$ as a function of \(x... [FREE SOLUTION]

Chapter 1: Problem 18

Graph $y$ as a function of $x$ by finding the slope and $y$-intercept of each line. $$y=\frac{2}{3} x-2$$

Short Answer

Expert verified

The graph of the function $y=\frac{2}{3}x-2$ is a straight line with a slope of $\frac{2}{3}$ and a y-intercept of -2, which passes through the points (0,-2) and (3,0).

Step by step solution

Identify the slope and y-intercept

In the given equation, $y=\frac{2}{3}x-2$, the slope $m$ is $\frac{2}{3}$ and the y-intercept $b$ is -2. This means that the line will cross the y-axis at -2.

Plot the y-intercept

First, plot the y-intercept on a graph. Start at the origin, (0,0), and move down 2 units (because it's negative) to arrive at the point (0,-2). Put a point there.

Use the slope to find another point

The slope is the ratio of the vertical change (rise) to the horizontal change (run). In this case, the slope is $\frac{2}{3}$, which means to move 2 units up and 3 units to the right. From the y-intercept point, do this to find the second point at (3,0).

Draw the line

Using your two points, draw a straight line that passes through them. This represents all the solutions for the equation $y=\frac{2}{3}x-2$.

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91影视

Graph \(y\) as a function of \(x\) by finding the slope and \(y\)-intercept of each line. $$y=\frac{2}{3} x-2$$

Short Answer

Step by step solution

Identify the slope and y-intercept

Plot the y-intercept

Use the slope to find another point

Draw the line

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