Identify the slope and y intercept. Then, graph the linear equation.

Question

`y+3=-4x`

Answer 1

To identify the slope and y-intercept from the given equation $y+3=-4x$, we first need to get the equation into the slope-intercept form, which is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

1. Isolate $y$: $$y+3=-4x$$ Subtract 3 from both sides: $$y=-4x-3$$

Now, we can identify the slope and y-intercept:

• The slope $m=-4$
• The y-intercept $b=-3$

Graphing the Equation

To graph the equation $y=-4x-3$:

1. Plot the y-intercept:

   • The y-intercept is the point where the line crosses the y-axis. Here, it is $(0,-3)$.

2. Use the slope to find another point:

   • The slope $-4$ can be expressed as $-4/1$. This means that for every 1 unit you move to the right on the x-axis, you move 4 units down on the y-axis.
   • Starting from the y-intercept $(0,-3)$:
     • Move 1 unit to the right to $x=1$
     • Move 4 units down to $y=-3-4=-7$
     • This gives us the point $(1,-7)$.

3. Plot the second point:

   • Plot the point $(1,-7)$.

4. Draw the line:

   • Connect these points with a straight line, extending it in both directions.

Here’s a summary of the points:

• Y-intercept: $(0,-3)$
• Another point: $(1,-7)$

Graph Description

The graph is a straight line that slopes downward from left to right (due to the negative slope). The line crosses the y-axis at $-3$.

If you'd like a visual representation, you can use graph paper or graphing software to plot the points and the line.