Could someone help me with finding an equation of the line containing the given pair of points (3,2) and (9,7)
(y-2)/(x-3) = (7-2)/(9-3)
y-2 = 5/6 (x-3)
First, find the slope using the formula y2-y1/x2-x1.
7 - 2/9 - 3
5 / 6---> slope
Use point-slope form: y - y1 = m (x - x1)
Use any one point:
y - 2 = 5/6 (x - 3)
Distributive property:
y - 2 = 5/6x - 15/6
Add 2 to each side:
y = 5/6x - 15/6 + 2/1
y = 5/6x - 1/2
To find the equation of the line containing the given pair of points (3,2) and (9,7), we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where "m" is the slope of the line and "b" is the y-intercept.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
For the points (3,2) and (9,7), we have:
m = (7 - 2) / (9 - 3)
Step 2: Substitute the coordinates of one of the points and the calculated slope into the slope-intercept form:
y - y1 = m(x - x1)
Using the point (3,2) and the slope m calculated in Step 1:
y - 2 = m(x - 3)
Step 3: Simplify the equation by distributing the slope:
y - 2 = m*x - 3m
Step 4: Move the constant term to the other side of the equation:
y = m*x - 3m + 2
This is the equation of the line containing the given pair of points (3,2) and (9,7).