Final answer:
The slope-intercept equation for the given line passing through (2,-7) and (6,-2) is y = (5/4)x - 19/2.
Step-by-step explanation:
To write the slope-intercept form of a linear equation, we need to find the slope and the y-intercept. The slope can be found using the formula: slope = (change in y)/(change in x). From the given points (2,-7) and (6,-2), we find the slope to be (−2−(−7))/(6−2) = 5/4. Next, we can use the point-slope form of the equation to find the equation of the line, which is: y - y1 = m(x - x1), where (x1, y1) is the given point (2,-7) and m is the slope. Substituting the values, we get y - (-7) = (5/4)(x - 2). Simplifying, we get y + 7 = (5/4)x - 5/2. Finally, rearranging the equation to the slope-intercept form, we have y = (5/4)x - 5/2 - 7, which simplifies to y = (5/4)x - 19/2.