We know that Priya will graph a line with the equation

y = \frac{3}{4} x - 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 = \frac{3}{4} x - 4

The

slope

of the line is

\frac{3}{4} .

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 = \frac{3}{4} x - 4

We will rewrite the equation so that the

y -

intercept is clearly visible.

y = \frac{3}{4} x + (- 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.

Exercise

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