a line passes through the points -3,1 and 6,5 write the equation of the line in slope intecept
To write the equation of the line in slope-intercept form, which is y = mx + b, we need to find the slope (m) and the y-intercept (b).
The slope (m) is determined by the formula:
m = (y2 - y1) / (x2 - x1)
Given the coordinates of the two points:
Point 1: (-3, 1)
Point 2: (6, 5)
Using the formula, we can find the slope:
m = (5 - 1) / (6 - (-3))
m = 4 / 9
Since we now have the slope (m), we can substitute it into the slope-intercept form and continue solving for the y-intercept (b).
y = mx + b
y = (4/9)x + b
To find the y-intercept (b), we can use one of the given points. Let's use (-3, 1).
1 = (4/9)(-3) + b
1 = -4/3 + b
To solve for b, we need to isolate it. Adding 4/3 to both sides, we get:
1 + 4/3 = b
7/3 = b
Now we know the slope (m) and the y-intercept (b), so the equation of the line in slope-intercept form is:
y = (4/9)x + 7/3
start with the two-point form and then just rearrange things as needed
y-5 = (5-1)/(6+3) * (x-6)