Write an equation of the line passing through (3,21)and (-4,-35) in the form of A x + B y = C. Where A, B and C are real numbers
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To find the equation of a line passing through two points, we can use the slope-intercept form (y = mx + b), where m represents the slope of the line, and b represents the y-intercept. However, to write the equation in the form of A x + B y = C, we need to rearrange the equation.
Step 1: Calculate the slope (m):
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
In this case, the given points are (3, 21) and (-4, -35).
m = (-35 - 21) / (-4 - 3)
m = (-56) / (-7)
m = 8
Step 2: Find the y-intercept (b):
To find the y-intercept, substitute the coordinates of one of the given points into the slope-intercept form (y = mx + b) and solve for b.
Using the point (3, 21):
21 = 8(3) + b
21 = 24 + b
b = -3
Step 3: Write the equation in the form of A x + B y = C:
Using the values of the slope (m) and the y-intercept (b) obtained from steps 1 and 2, respectively, we can write the equation in slope-intercept form:
y = 8x - 3
To convert this equation into the form A x + B y = C, we need to rearrange it by moving the x term to the left side:
-8x + y = -3
Multiply both sides by -1:
8x - y = 3
Therefore, the equation of the line passing through (3, 21) and (-4, -35) in the form of A x + B y = C is:
8x - y = 3, where A = 8, B = -1, and C = 3.