Final answer:
The slope-intercept form for the line containing the points (3,5) and (2,−5) is y = 10x - 25. The slope (m) was calculated as 10, and then the slope-intercept form was obtained by using one of the given points.
Step-by-step explanation:
To identify the equation in slope-intercept form for the line containing the points (3,5) and (2,−5), we first need to calculate the slope (m) of the line using the formula m = ∆y / ∆x, where ∆y is the change in y-values and ∆x is the change in x-values. For the points (3,5) and (2,−5), the slope m is calculated as (5 - (−5)) / (3 - 2) = 10.
With the slope, we can then use the point-slope form, y - y1 = m(x - x1), and substitute one of the given points and the slope to get the equation of the line. Let's use the point (3,5), thus y - 5 = 10(x - 3). Simplify this to get the slope-intercept form, y = 10x - 30 + 5, which further simplifies to y = 10x - 25.
Therefore, the slope-intercept form of the equation for the line that goes through the points (3,5) and (2,−5) is y = 10x - 25.