4. Write the equation of a line whose slope is 6 and whose y intercept is -3.
The answer would be y=6x-3
This is the y-intercept formula (y=mx+b) where m is the slope and b is the y-intercept.
Thanx
What about this one?Can you plz help?
6. What happens to the graph of the line y = 3x -2 when the equation is changed to y = 3x +6?
The slope stays the same, but the second line starts higher. Therefore, the 2 lines are parallel.
To explain how to determine what happens to the graph of the line when the equation changes, we need to understand the equation for a line in slope-intercept form, which is y = mx + b.
In this case, the original equation is y = 3x - 2 and the changed equation is y = 3x + 6.
The slope (m) in both equations is 3, which means the lines have the same steepness or inclination. The slope is the coefficient of x, and it determines how the line moves vertically and horizontally.
The y-intercept (b) in the original equation is -2, which means the line intersects the y-axis at the point (0, -2). In the changed equation, the y-intercept is 6, meaning the line intersects the y-axis at the point (0, 6).
When comparing these two equations, we can see that the slope remains the same, indicating that the lines have the same steepness or inclination. However, the changed equation has a y-intercept that is higher, resulting in the line starting at a higher point on the y-axis.
Visually, this means that the second line will be parallel to the original line but shifted upwards. Both lines will have the same slope, but they won't intersect and will maintain a constant distance between them.
So in summary, when the equation is changed to y = 3x + 6, the graph of the line remains parallel to the original line but starts higher on the y-axis.