Find an equation of the line passing through each of the following pairs of points.
Find an equation of the line passing through each of the following pairs of points.
Find an equation of the line passing through each of the following pairs of points.
clearly the slope is (3-0)/(4-0) = 3/4 and since (0,0) is on the y-axis the y-intercept is 0
what do you know about the values of m and b in y = mx + b ?
When in danger or in doubt, sketch a graph :)
To find the equation of a line passing through two points, we can use the slope-intercept form of a line, which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)
Once we have the slope (m), we can substitute one of the points into the equation, along with the slope, to solve for the y-intercept (b).
Let's find the equations for the given pairs of points:
Pair 1: (2, 3) and (4, 5)
Let's label the first point as (x1, y1) = (2, 3) and the second point as (x2, y2) = (4, 5).
Using the formula for slope (m):
m = (y2 - y1) / (x2 - x1)
m = (5 - 3) / (4 - 2)
m = 2 / 2
m = 1
Now, substituting one of the points (let's use (2, 3)) into the slope-intercept form (y = mx + b):
3 = 1(2) + b
3 = 2 + b
Solving for b:
b = 3 - 2
b = 1
The equation of the line passing through the points (2, 3) and (4, 5) is:
y = x + 1
Similarly, you can find the equations for other pairs of points using the same method.