Question

graph the linear function using slope-intercept form.

1. ( y = 2x + 6 )

Explanation:

Step1: Recall 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. For the equation $y = 2x+6$, we can identify that the slope $m = 2$ (or $\frac{2}{1}$) and the y - intercept $b = 6$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Since $b = 6$, we plot the point $(0,6)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m=\frac{\text{rise}}{\text{run}}=\frac{2}{1}$. From the point $(0,6)$, we move up 2 units (because the rise is 2) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,6+2)=(1,8)$. We can also move down 2 units and left 1 unit from $(0,6)$ to get another point, for example, $(0 - 1,6 - 2)=(- 1,4)$.

Step4: Draw the line

Using a straightedge, draw a line that passes through the points we have plotted (such as $(0,6)$ and $(1,8)$ or other points found using the slope). This line represents the graph of the linear function $y = 2x+6$.

Answer:

To graph $y = 2x + 6$:

1. Plot the y - intercept at $(0,6)$ (since $b = 6$ in $y=mx + b$).
2. Use the slope $m = 2=\frac{2}{1}$: from $(0,6)$, move up 2 units and right 1 unit to get $(1,8)$, or down 2 units and left 1 unit to get $(-1,4)$.
3. Draw a straight line through these (and other) points. The line has a slope of 2 and crosses the y - axis at $(0,6)$.