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Chapter 1: Problem 21

Find the slope and \(y\) -intercept (if possible) of the equation of the line. Sketch the line. $$5 x-2=0$$

Short Answer

Expert verified
The given equation is a vertical line that does not present a slope or a y-intercept. The x-intercept is located at 0.4, or (0.4, 0) in Cartesian coordinates. This line is vertical and parallels the y-axis, passing through the point (0.4, 0).

Step by step solution

01

Understanding the Equation

The given equation is 5x-2=0. This equation provides the value of the x-coordinate of the pointed line, rather than a typical linear equation (y=mx+b, where m is the slope and b is the y-intercept). It's a vertical line equation, and we should recognize that vertical lines do not have a typical slope or y-intercept.
02

Find the x-intercept

Given the equation 5x-2=0, we can solve for x by adding 2 to both sides and then dividing by 5. That would give us x = 2/5 or 0.4.
03

Sketch the line

To sketch this line, we will simply draw a line passing through the x-coordinate 0.4 and paralleling the y-axis as it is vertical. It will cross the x-axis at point (0.4,0), which is the x-intercept of this line. The line will extend infinitely in both the positive and negative y-directions, as the equation does not specify a y-bound.

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