Indicate in standard form the equation of the line passing through the given points.
G(4, 6), H(1, 5)
line equals (1,-3)
this is the easiest way based on the fact that for
Ax + By + C = 0, the slope is -A/B
slope of line is (6-5)/(4-1) = 1/3
so the equation must be
x - 3y + c = 0
plug in (1,5)
1-15 + c = 0
c = 14
so x - 3y + 14 = 0
from there you can change it to any form that was asked for
To find the equation of the line passing through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, m represents the slope of the line, and b represents the y-intercept.
Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's label the coordinates of point G as (x1, y1) = (4, 6) and the coordinates of point H as (x2, y2) = (1, 5).
Substituting these values into the formula, we get:
m = (5 - 6) / (1 - 4)
m = -1 / -3
m = 1/3
Step 2: Use the slope-intercept form to find the equation:
Choose one of the points, G or H, and substitute the values of the coordinates into the equation y = mx + b.
Let's use point G (4, 6):
6 = (1/3) * 4 + b
Step 3: Solve for b:
6 = 4/3 + b
6 - 4/3 = b
18/3 - 4/3 = b
14/3 = b
Now that we have the value of b, we can write the equation using the slope and y-intercept:
y = (1/3)x + 14/3
To represent the equation in standard form, we need to eliminate fractions and rewrite the equation as Ax + By = C, where A, B, and C are integers and A is positive.
Multiply both sides of the equation by 3 to eliminate the fractions:
3y = x + 14
Rearrange the terms by moving x to the left side:
-x + 3y = 14
Since A (coefficient of x) should be positive, we will multiply both sides of the equation by -1:
x - 3y = -14
Therefore, the equation of the line passing through the points G(4, 6) and H(1, 5) in standard form is x - 3y = -14.