Find an equation of the line containing the given pair of points. (1/4,-1/2) and (3/4,5). What is the equation of the line? y=
Thank you for all your help.
(1/4, -1/2), (3/4, 5).
m = (5 + 1/2) / (3/4 - 1/4)
m = 5 1/2 / (1/2),
m = (11/2) / (1/2),
m = 11/2 * 2/1 = 22/2 = 11.
y = mx + b,
11(1/4) + b = -1/2,
11/4 + b = -1/2,
b = -1/2 - 11/4 = -2/4 - 11/4 = -13/4.
y = 11x - 13/4.
(11 - 7) 5
To find the equation of a line passing through two given points, you can use the slope-intercept form of a linear equation:
y = mx + b
where m represents the slope of the line and b represents the y-intercept.
Step 1: Find the slope.
The slope (m) can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of the given points.
Given points: (1/4, -1/2) and (3/4, 5)
Substituting the coordinates into the slope formula:
m = (5 - (-1/2)) / (3/4 - 1/4)
m = (5 + 1/2) / (3/4 - 1/4)
m = (11/2) / (2/4)
m = (11/2) / (1/2)
m = (11/2) * (2/1)
m = 11
Step 2: Find the y-intercept (b).
To find the y-intercept, select one of the given points and substitute its coordinates (x, y) into the equation y = mx + b. Solve for b.
Using the point (1/4, -1/2):
-1/2 = 11(1/4) + b
-1/2 = 11/4 + b
To remove fractions, multiply through by 4:
-2 = 11 + 4b
Rearranging the equation:
4b = -13
b = -13/4
Step 3: Write the equation.
Now that we know the slope (m = 11) and the y-intercept (b = -13/4), we can write the equation of the line:
y = 11x - 13/4
Therefore, the equation of the line passing through the points (1/4, -1/2) and (3/4, 5) is y = 11x - 13/4.