Question

graph $y = -5x$.

Explanation:

Step1: Identify the 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. For the equation $y=-5x$, we can rewrite it as $y=-5x + 0$. So, the slope $m=-5$ and the y - intercept $b = 0$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Since $b = 0$, the line passes through the point $(0,0)$ (the origin).

Step3: Use the slope to find another point

The slope $m=\frac{\text{rise}}{\text{run}}=-5=\frac{-5}{1}$. From the point $(0,0)$, we can move down 5 units (because the rise is - 5, which means a decrease of 5) and then 1 unit to the right (because the run is 1). This gives us the point $(1,-5)$. We can also use the slope in the opposite direction: move up 5 units and 1 unit to the left. From $(0,0)$, moving up 5 units and 1 unit to the left gives us the point $(- 1,5)$.

Step4: Draw the line

After plotting the points (for example, $(0,0)$ and $(1,-5)$ or $(0,0)$ and $(-1,5)$), we draw a straight line passing through these points.

To graph $y = - 5x$:

1. Start at the origin $(0,0)$ (since the y - intercept $b = 0$).
2. Use the slope $m=-5$ (which can be thought of as $\frac{\text{change in }y}{\text{change in }x}=\frac{-5}{1}$). From $(0,0)$, move 1 unit to the right (increase $x$ by 1) and 5 units down (decrease $y$ by 5) to get the point $(1, - 5)$. Or move 1 unit to the left (decrease $x$ by 1) and 5 units up (increase $y$ by 5) to get the point $(-1,5)$.
3. Draw a straight line through the origin and the other point (either $(1,-5)$ or $(-1,5)$) to represent the line $y=-5x$.

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through the origin with a slope of - 5. If we were to describe the key points, the line passes through $(0,0)$ and $(1, - 5)$ (or other points determined by the slope from the origin).)

Answer:

Step1: Identify the 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. For the equation $y=-5x$, we can rewrite it as $y=-5x + 0$. So, the slope $m=-5$ and the y - intercept $b = 0$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Since $b = 0$, the line passes through the point $(0,0)$ (the origin).

Step3: Use the slope to find another point

The slope $m=\frac{\text{rise}}{\text{run}}=-5=\frac{-5}{1}$. From the point $(0,0)$, we can move down 5 units (because the rise is - 5, which means a decrease of 5) and then 1 unit to the right (because the run is 1). This gives us the point $(1,-5)$. We can also use the slope in the opposite direction: move up 5 units and 1 unit to the left. From $(0,0)$, moving up 5 units and 1 unit to the left gives us the point $(- 1,5)$.

Step4: Draw the line

After plotting the points (for example, $(0,0)$ and $(1,-5)$ or $(0,0)$ and $(-1,5)$), we draw a straight line passing through these points.

To graph $y = - 5x$:

1. Start at the origin $(0,0)$ (since the y - intercept $b = 0$).
2. Use the slope $m=-5$ (which can be thought of as $\frac{\text{change in }y}{\text{change in }x}=\frac{-5}{1}$). From $(0,0)$, move 1 unit to the right (increase $x$ by 1) and 5 units down (decrease $y$ by 5) to get the point $(1, - 5)$. Or move 1 unit to the left (decrease $x$ by 1) and 5 units up (increase $y$ by 5) to get the point $(-1,5)$.
3. Draw a straight line through the origin and the other point (either $(1,-5)$ or $(-1,5)$) to represent the line $y=-5x$.

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through the origin with a slope of - 5. If we were to describe the key points, the line passes through $(0,0)$ and $(1, - 5)$ (or other points determined by the slope from the origin).)