Final answer:
To find the equation of a line passing through two given points, calculate the slope using the formula (m = (y2 - y1)/(x2 - x1)), then substitute the slope and the coordinates of one of the points into the equation y = mx + b to solve for the y-intercept (b). Finally, substitute the slope and y-intercept into the equation to obtain the equation of the line.
Step-by-step explanation:
To determine the equation of a line that passes through two given points, we can use the formula for the slope-intercept form of a linear equation: y = mx + b.
1. Start by finding the slope (m) of the line using the formula (m = (y2 - y1)/(x2 - x1)). Use the coordinates of the given points to calculate the slope.
2. Once you have the slope, substitute it into the equation along with the coordinates of one of the given points to find the value of the y-intercept (b).
3. Finally, substitute the slope and y-intercept into the equation y = mx + b to obtain the equation of the line.
For example, let's find the equation of the line passing through (-4, 6) and (5, -1).
1. slope (m) = (-1 - 6)/(5 - (-4)) = -7/9
2. Using the coordinates (-4, 6), we can substitute the values into y = mx + b to solve for b: 6 = (-7/9)(-4) + b. Solving for b, we get b = 42/9
3. Substitute the values of m and b into the equation y = mx + b to obtain the equation: y = (-7/9)x + 42/9. The equation of the line passing through (-4, 6) and (5, -1) is y = (-7/9)x + 42/9.