Final answer:
The linear equation 4x+y=0 has the slope -4 and both x-intercept and y-intercept at (0,0), with the slope-intercept form being y = -4x.
Step-by-step explanation:
The equation given is 4x+y=0. To find the slope and y-intercept of this linear equation, we first want to put it in the slope-intercept form, which is y = mx + b. Here, m represents the slope and b represents the y-intercept. First, we solve for y by isolating it on one side of the equation:
y = -4x + 0
From this new equation, it is clear that the slope (m) is -4, as it is the coefficient of x. The y-intercept (b) is 0 because it's the constant in the equation. To find the x-intercept, we set y to 0 and solve for x, which gives us x = 0. Therefore, the x-intercept is also at (0,0), which is the same as the y-intercept in this case.
- Direction: Since the slope is negative, the line slants downwards from left to right.
- Slope: -4
- Y-intercept: (0,0)
- X-intercept: (0,0)
- Slope-Intercept Form: y = -4x