Final answer:
To write the equation of a line in slope-intercept form, find the slope using two given points and then substitute the slope and one point into the equation. The equation of the line passing through (-2, -1) and (19, 14) is y = (5/7)x + 3/7.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the given points (-2, -1) and (19, 14), we can find the slope as follows: m = (14 - (-1)) / (19 - (-2)) = 15 / 21 = 5/7.
We can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Substituting the slope (5/7) and one of the points (-2, -1) into the equation, we can solve for b:
- -1 = (5/7)(-2) + b
- -1 = -10/7 + b
- b = -1 + 10/7
- b = -7/7 + 10/7
- b = 3/7
Therefore, the equation of the line in slope-intercept form is y = (5/7)x + 3/7.
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