Final answer:
The equation of a line with a given slope can be found using the slope-intercept form y = mx + b. By replacing the slope (m) and the coordinates of a known point into the formula, we can solve for b and write the complete equation. Another point on this line is found by choosing any x-value and calculating the corresponding y-value.
Step-by-step explanation:
To find the equation of a line with a known slope, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. If we are given a point through which the line passes, we can substitute the x and y values of that point into the equation along with the slope to solve for b. Once that is done, we have a complete equation of the line.
To find another point on the line, you can simply choose any x-value and substitute it back into the equation to solve for the corresponding y-value, which will give you the coordinates of another point on the line.
As an example, if the slope is 2 and the line passes through the point (6.4, 2000), we would use these in the slope-intercept form:
y = 2x + b
2000 = 2(6.4) + b
2000 = 12.8 + b
b = 1987.2
Thus, the equation of the line is y = 2x + 1987.2. Another point on this line could be found by picking any x-value, for example, x = 10 gives us y = 2(10) + 1987.2 = 2027.2, so the point (10, 2027.2) also lies on this line.