Find an equation of the line that passes through the given points. (Let x be the independent variable and y be the dependent variable.)
(3, 13) and (4, 20)
y=mx+b
13=m*3+b and the second equation gives
20=m*4+b
subtract first from second
m=7
then for b
13=7*3+b solve for b.
slope = (20-13)/(4-3) = 7
also for any (x,y)
slope = (y-20)/(x-4)
so
7 = (y-20)/(x-4)
7 x - 28 = y - 20
so
y = 7 x -8
Good, you have two different ways now :)
To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.
To find the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (3, 13) and (4, 20), we can plug in the values into the slope formula:
m = (20 - 13) / (4 - 3)
m = 7 / 1
m = 7
Now that we have the slope, we can use one of the points and the slope to find the y-intercept (b). Let's use the point (3, 13) and substitute the values into the equation y = mx + b:
13 = 7(3) + b
Simplifying the equation:
13 = 21 + b
b = 13 - 21
b = -8
Now we have the slope (m = 7) and the y-intercept (b = -8). Substituting these values back into the slope-intercept form, we get the equation of the line that passes through the given points:
y = 7x - 8