The line is increasing and it crosses the y-axis below the origin. It passes through Quadrants I, III, and IV.
Practice makes perfect
We know that Priya will graph a line with the equation y= 34x - 4. We want to describe how the line will look like, including the quadrants that the line will pass through. The equation is given in slope-intercept form. Let's start by focusing on its slope.
y= 3/4x - 4
The slope of the line is 34. Recall that when a slope is positive, the relationship between x and y is increasing. When a slope is negative — the relationship is decreasing. In Priya's case the slope is positive, so the relationship in increasing. Now, we will focus on the y-intercept of the equation.
y=3/4x - 4
We will rewrite the equation so that the y-intercept is clearly visible.
y=3/4x + ( - 4)
The y-intercept of the line is - 4. The y-intercept is the y-coordinate of the point on a graph where the line crosses the y-axis. Therefore, when the y-intercept is negative, the line must cross the y-axis in a point with a negative y-coordinate. This means that the line crosses the y-axis below the origin.
Conclusions
The line that Priya will graph is increasing and it crosses the y-axis below the origin. Let's sketch how more or less these types of graphs look.
All lines that are increasing and cross the y-axis below the origin pass through Quadrants I, III, and IV. Therefore Priya's graph also will pass through Quadrants I, III, and IV.
