Question

I

A line passes through the points (4, 10) and (12, 8). Which shows an equation for this line written in
standard form?
x + y = -9
4
²x+y=11
4
-²x+y=-11
x+y=9
4
91
IN

Answer 1

To find the equation of the line passing through the points (4,10) and (12,8), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point and m is the slope.

Step 1: Find the slope (m):

The slope (m) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Let's use the points (4,10) and (12,8):

m = (8 - 10) / (12 - 4)

m = -2 / 8

m = -1/4

Step 2: Use one point to write the equation:

Let's use the point (4,10):

y - 10 = (-1/4)(x - 4)

Step 3: Convert to standard form:

To convert to standard form, we need to eliminate fractions and rearrange the equation in the form Ax + By = C.

Multiply both sides of the equation by 4 to eliminate the fraction:

4(y - 10) = -1(x - 4)

4y - 40 = -x + 4

Rearrange the equation to isolate x and y terms on the left side:

x + 4y = 44

Therefore, the equation of the line passing through the points (4,10) and (12,8) in standard form is:

x + 4y = 44

The correct answer is option x + 4y = 44.

Explanation: