Determine the slope (-3,-4) m =2
We can use the slope-intercept form of a linear equation, y = mx + b, to determine the equation of the line. Given that the slope (m) is 2 and a point (-3, -4) lies on the line, we can substitute these values into the equation and solve for the y-intercept (b).
Using the point-slope form:
y - y1 = m(x - x1)
Plugging in the values:
y - (-4) = 2(x - (-3))
Simplifying:
y + 4 = 2(x + 3)
Distributing the 2:
y + 4 = 2x + 6
Subtracting 4 from both sides:
y = 2x + 2
Therefore, the equation of the line is y = 2x + 2.
To determine the slope, you need the coordinates of two points on the line. In this case, the two points given are (-3, -4) and another point that is not provided. Without the second point, it's not possible to calculate the slope definitively.
However, if you are given a slope of 2 and a point on the line (-3, -4), you can determine a second point. First, you need to understand that the slope represents the ratio of the vertical change to the horizontal change between two points on the line. In other words, for every 2 units of vertical change, there is 1 unit of horizontal change.
Starting from the point (-3, -4), you can use the slope to find the coordinates of another point on the line. You can apply the slope as follows:
- Start at (-3, -4) as your initial point.
- Move 2 units up and 1 unit to the right. This will give you the coordinates (-2, -2).
- Connect the two points (-3, -4) and (-2, -2) to form a line segment.
- The line segment represents a portion of the line with a slope of 2 passing through the point (-3, -4).
Note that the line extends infinitely in both directions, but without additional information, we cannot determine the exact equation of the line or identify other points on the line.
To determine the slope of a line given two points, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (-3, -4) and the slope m = 2, we can substitute the values into the formula:
m = (y2 - y1) / (x2 - x1)
2 = (y2 - (-4)) / (x2 - (-3))
Let's solve for the coordinates of the second point:
x2 = x1 + (y2 - y1) / m
x2 = -3 + (y2 - (-4)) / 2
x2 = -3 + (y2 + 4) / 2
2x2 = -6 + y2 + 4
2x2 - y2 = -2
Now let's substitute the coordinates (-3,-4) into the equation:
2(-3) - (-4) = -2
-6 + 4 = -2
-2 = -2
The equation is true, which means the given points (-3, -4) satisfy the equation, and the slope is indeed equal to 2.