Final answer:
The equation in slope-intercept form using the input-output pairs (-5, 9) and (5, 11) is y = (1/5)x + 10.
Step-by-step explanation:
The goal is to write an equation in slope-intercept form using two input-output pairs, (-5, 9) 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 given points, we find the slope to be (11 - 9) / (5 - (-5)) which simplifies to 2 / 10, further simplifying to 1/5. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope, so we need to find the y-intercept (b). Using one of the points, say (-5, 9), we plug them into the equation 9 = (1/5)(-5) + b. This simplifies to 9 = -1 + b; adding 1 to both sides gives us b = 10. Therefore, the equation of the line in slope-intercept form is y = (1/5)x + 10.