Question

graph the line with the equation $y = \frac{6}{5}x - 2$.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=-2$. So the y-intercept is the point $(0, -2)$.

Step2: Identify slope

The slope $m=\frac{6}{5}$, meaning $\frac{\text{rise}}{\text{run}}=\frac{6}{5}$.

Step3: Find second point

From $(0, -2)$, move 5 units right (run) and 6 units up (rise): $x=0+5=5$, $y=-2+6=4$. This gives the point $(5, 4)$.

Step4: Plot and connect points

Plot $(0, -2)$ and $(5, 4)$, then draw a straight line through them, extending it across the grid.

Answer:

The line passes through $(0, -2)$ and $(5, 4)$, and extends infinitely in both directions on the coordinate plane.