Final answer:
To find the equation of the line passing through (-5,-3) and (5,11), calculate the slope using the coordinates then apply it to the point-slope formula. Simplify to write the equation in slope-intercept form, resulting in y = 1.4x + 10.
Step-by-step explanation:
To find the equation of a line passing through two given points, (-5,-3) and (5,11). To do this, we first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the points, we get m = (11 - (-3)) / (5 - (-5)) = 14 / 10 = 1.4.
With the slope and one of the given points, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), to write the equation of the line. Substituting the slope and the coordinates of the first point (-5,-3), we get y - (-3) = 1.4(x - (-5)). Simplifying, we find y + 3 = 1.4x + 7.
Finally, we write the equation in slope-intercept form, y = mx + b, by isolating y: y = 1.4x + 10. Therefore, the equation of the line passing through the points (-5,-3) and (5,11) is y = 1.4x + 10.