Question

graph the equation using the slope and the y - intercept.
( y = \frac{6}{5}x + 5 )
choose the correct graph on the right.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b$ is the y-intercept. For $y=\frac{6}{5}x + 5$, the y-intercept is $b=5$. This means the line crosses the y-axis at $(0,5)$.

Step2: Identify slope

The slope $m=\frac{6}{5}$, which is positive. A positive slope means the line rises from left to right. The slope $\frac{6}{5}$ means for a run of $5$ units right, the line rises $6$ units up.

Step3: Match to options

• Option A and C have negative slopes (fall left to right), so they are eliminated.
• Option B has a y-intercept below 0, not 5.
• Option D has a positive slope and crosses the y-axis at $(0,5)$, matching the equation.

Answer:

D. <The graph with a positive slope rising from left to right, crossing the y-axis at (0,5)>