Question

Sketch a graph of the equation. $$ y-2=\frac{3}{2}(x-1) $$

Short answer

The graph of the equation \(y-2=\frac{3}{2}(x-1)\) is a line with slope \(\frac{3}{2}\) that passes through the point (1, 2). The line rises 3 units and runs 2 units to the right.

Step-by-step solution

Identify the slope and the point

In this equation \( y - 2 = \frac{3}{2}(x - 1) \), the slope \( m \) is \(\frac{3}{2}\) and the point that the line passes through is \((1,2)\). So, the line rises by 3 units and runs 2 units to the right.

Plot the point

Start by placing a point at the coordinates (1,2) on the graph.

Use the slope to find the next point

From the point (1,2), move 3 units up (because the slope's numerator is 3) and 2 units to the right (because the slope's denominator is 2). This gives the new point (3,5). Place this point on your graph.

Draw the Line

Now that you have two points, you can draw a straight line through them, making sure it extends beyond both points and arrows are placed at either end, indicating that the line extends indefinitely.