Final answer:
The slope-intercept form of the equation passing through the points (7, -3) and (-35, -21) is y = 3/7x - 4. The slope was calculated using the formula and the y-intercept was found by substituting the slope and one point into the slope-intercept equation.
Step-by-step explanation:
To calculate the slope-intercept form (y = mx + b) of the equation of a line passing through two points, we need to find out the slope (m) and the y-intercept (b).
First, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points. Substituting values for our points (7, -3) and (-35, -21), the slope m = (-21 - (-3)) / (-35 - 7) = -18 / -42 = 3/7.
Next, to find 'b', plug the value of the slope and the coordinates of one of the points into the slope-intercept equation. For point (7, -3), -3 = 3/7*7+b simplifies to b = -4.
Therefore, the equation of the line in slope-intercept form is y = 3/7x - 4.
Learn more about Slope-Intercept Form