which graph represents the function $y - 3=\frac{3}{2}(x - 4)$?
which graph represents the function $y - 3=\frac{3}{2}(x - 4)$?
Answer
Explanation:
Step1: Rewrite in slope - intercept form
Starting with $y - 3=\frac{3}{2}(x - 4)$, distribute the $\frac{3}{2}$: $y-3=\frac{3}{2}x-6$. Then add 3 to both sides to get $y=\frac{3}{2}x - 3$.
Step2: Identify slope and y - intercept
The slope $m=\frac{3}{2}$ (positive slope means the line rises from left to right) and the y - intercept $b=-3$ (the line crosses the y - axis at the point $(0, - 3)$).
Answer:
The graph with a positive slope and y - intercept at $(0,-3)$ (the third graph from the left among the given options assuming a standard orientation of graphs where positive - slope lines rise from left to right and the y - intercept is correctly placed).