Final answer:
The equation of the line passing through the points (-5,17) and (-3,13) is y = -2x + 7. This is found by calculating the slope of the line and using one of the points to write the equation in point-slope form, then simplifying it to slope-intercept form.
Step-by-step explanation:
To find an equation of the line passing through the points (-5,17) and (-3,13), we first need to find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of the points.
So, the slope m = (13 - 17) / (-3 + 5) = -4 / 2 = -2.
Next, we use the point-slope form of the line equation, which is y - y1 = m(x - x1), substituting in the slope we found and the coordinates of one of the points.
For example, using the point (-5,17), the equation becomes y - 17 = -2(x + 5).
To write this in the slope-intercept form y = mx + b, simplify to get y = -2x - 10 + 17, which is y = -2x + 7.
Therefore, the equation of the line is y = -2x + 7.