Final answer:
The equation of the line that passes through the points (-5,0) and (2,-3) is found by first calculating the slope which is -3/7 and then using the point-slope form, resulting in y = (-3/7)x - 15/7.
Step-by-step explanation:
Finding the Equation of a Line
To find the equation of a line that passes through two given points (-5,0) and (2,-3), you first need to determine the slope of the line. The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points, we have m = (-3 - 0) / (2 - (-5)) = -3 / 7. With the slope and one of the points, we can use the point-slope form of an equation of a line, y - y1 = m(x - x1), to write the equation of the line. Substituting the point (-5, 0) and the slope -3/7 into the point-slope form, we get y - 0 = (-3/7)(x - (-5)), or y = (-3/7)x - 15/7.
This is the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In conclusion, the equation of the line that passes through the points (-5,0) and (2,-3) is y = (-3/7)x - 15/7.