Questions: Graphing a line by first finding its slope and y-intercept The equation of a line is given below. -6x-2y=-8 Find the slope and the y-intercept. Then use them to graph the line. slope: y-intercept:

Solution Steps

The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We are given the equation $-6x - 2y = -8$. To rewrite this equation in slope-intercept form, we need to isolate $y$. First, add $6x$ to both sides of the equation: $-2y = 6x - 8$

Next, divide both sides by $-2$: $y = \frac{6x - 8}{-2}$ $y = -3x + 4$

Now that the equation is in slope-intercept form ($y = mx + b$), we can identify the slope and y-intercept. The slope $m$ is the coefficient of $x$, which is $-3$. The y-intercept $b$ is the constant term, which is $4$.

To graph the line, we start by plotting the y-intercept, which is the point $(0, 4)$. From the y-intercept, we use the slope to find another point on the line. The slope is $-3$, which can be written as $\frac{-3}{1}$. This means that for every 1 unit we move to the right along the x-axis, we move 3 units down along the y-axis. So, starting at $(0, 4)$, we move 1 unit to the right and 3 units down to find the point $(1, 1)$. Plot the point $(1, 1)$. Draw a line through the points $(0, 4)$ and $(1, 1)$.

Final Answer: