Find an equation in slope-intercept form passing through the (2,5) and (7, -3).
since you have two points, you can get the slope:
(-3-5)/(7-2) = -8/5
Now, the slope never changes, so, you can pick any other point (x,y) on the line, and figure the slope through (2,5) and (x,y) the same way:
(y-5)/(x-2) = -8/5
Now just rearrange things the way you want.
y-5 = -8/5 (x-2)
y-5 = -8/5 x + 16/5
y = -8/5 x + 41/5
Juan says, "When you put together unequal groups, you can only add." Is he correct? Explain.
To find an equation in slope-intercept form passing through two given points, you need to find the slope and the y-intercept of the line.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given points (2, 5) and (7, -3):
slope = (-3 - 5) / (7 - 2)
slope = -8 / 5
Now, we have the slope of the line. The slope-intercept form of an equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the y-intercept, we can substitute one of the given points into the slope-intercept equation and solve for b. Let's use the point (2, 5):
5 = (-8/5) * 2 + b
5 = -16/5 + b
5 + 16/5 = b
(25/5) + (16/5) = b
(25 + 16)/5 = b
41/5 = b
So, the y-intercept, b, is equal to 41/5.
Now, substitute the slope and y-intercept into the slope-intercept form equation to get the final equation:
y = (-8/5)x + (41/5)
Therefore, the equation in slope-intercept form passing through the points (2,5) and (7, -3) is y = (-8/5)x + (41/5).