Question

graph the line.

y - 4x = -2

Explanation:

Step1: Rewrite in slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Starting with the given equation $y-4x=-2$, we add $4x$ to both sides of the equation.
So, $y = 4x-2$.

Step2: Identify slope and y - intercept

From the equation $y = 4x - 2$, the slope $m = 4$ (which can be written as $\frac{4}{1}$) and the y - intercept $b=-2$. The y - intercept means the line crosses the y - axis at the point $(0, - 2)$.

Step3: Find another point using slope

Using the slope $\frac{4}{1}$ (rise over run), from the point $(0,-2)$, we move up 4 units (since the numerator of the slope is 4) and to the right 1 unit (since the denominator of the slope is 1). This gives us the point $(0 + 1,-2 + 4)=(1,2)$.

Step4: Graph the line

Plot the points $(0,-2)$ and $(1,2)$ on the coordinate plane. Then, draw a straight line passing through these two points.

(Note: Since the actual graphing is a visual task, the key steps are to find the two points and then draw the line through them. The final answer in terms of the graph is the line passing through $(0, - 2)$ and $(1,2)$ with a slope of 4.)

Answer:

Step1: Rewrite in slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Starting with the given equation $y-4x=-2$, we add $4x$ to both sides of the equation.
So, $y = 4x-2$.

Step2: Identify slope and y - intercept

From the equation $y = 4x - 2$, the slope $m = 4$ (which can be written as $\frac{4}{1}$) and the y - intercept $b=-2$. The y - intercept means the line crosses the y - axis at the point $(0, - 2)$.

Step3: Find another point using slope

Using the slope $\frac{4}{1}$ (rise over run), from the point $(0,-2)$, we move up 4 units (since the numerator of the slope is 4) and to the right 1 unit (since the denominator of the slope is 1). This gives us the point $(0 + 1,-2 + 4)=(1,2)$.

Step4: Graph the line

Plot the points $(0,-2)$ and $(1,2)$ on the coordinate plane. Then, draw a straight line passing through these two points.

(Note: Since the actual graphing is a visual task, the key steps are to find the two points and then draw the line through them. The final answer in terms of the graph is the line passing through $(0, - 2)$ and $(1,2)$ with a slope of 4.)