Question

graph the following features: • y-intercept = 4 • slope = 2

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the y - intercept $b = 4$ and the slope $m=2$, the equation of the line is $y=2x + 4$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=4$. So we plot the point $(0,4)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 2=\frac{\text{rise}}{\text{run}}=\frac{2}{1}$. From the point $(0,4)$, we can move up 2 units (rise) and 1 unit to the right (run) to get the next point. So from $(0,4)$, adding 1 to the $x$ - coordinate and 2 to the $y$ - coordinate, we get the point $(0 + 1,4+ 2)=(1,6)$. We can also move down 2 units and 1 unit to the left from $(0,4)$ to get the point $(- 1,2)$ (since $\frac{-2}{-1}=2$).

Step4: Draw the line

Draw a straight line passing through the points we have plotted (e.g., $(0,4)$ and $(1,6)$ or $(0,4)$ and $(-1,2)$) to represent the linear equation $y = 2x+4$.

Answer:

To graph the line:

1. Plot the point \((0, 4)\) (the y - intercept).
2. Using the slope \(2=\frac{2}{1}\), from \((0, 4)\), move 1 unit right and 2 units up to plot \((1, 6)\) (or 1 unit left and 2 units down to plot \((-1, 2)\)).
3. Draw a straight line through these points. The equation of the line is \(y = 2x+4\).