Question

1. \\(y = \frac{3}{4}x + 1\\)

Explanation:

Identify the equation form

Using the Slope-Intercept Form knowledge point

$$ y = mx + b $$

$$ m = \frac{3}{4},\quad b = 1 $$

Determine the y-intercept

Using the y-intercept knowledge point

$$ (0, b) = (0, 1) $$

Apply the slope to find a second point

Using the Slope Formula knowledge point

$$ \text{slope } m = \frac{\text{rise}}{\text{run}} = \frac{3}{4} $$

$$ (x_2, y_2) = (0 + 4, 1 + 3) = (4, 4) $$

Draw the line through the points

Using the Graphing Linear Equations knowledge point

$$ \text{Line passes through } (0, 1) \text{ and } (4, 4). $$

Answer:

The linear equation is \(y = \frac{3}{4}x + 1\).

To graph this line:

1. Plot the \(y\)-intercept at \((0, 1)\).
2. Use the slope \(m = \frac{3}{4}\) to move up 3 units and right 4 units to plot a second point at \((4, 4)\).
3. Draw a straight line passing through both points.