Question

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (1, 1) and (3, 4)

Answer 1

To find the standard form of a line that goes through (1, 1) and (3, 4), first calculate the slope, then use point-slope form, and finally, rearrange to standard form to get -3x + 2y = -1.

Step-by-step explanation:

Finding the Equation of a Line in Standard Form

The task is to find the standard form of the line that passes through the points (1, 1) and (3, 4). First, we calculate the slope (m) using the formula:

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

Substituting in our points gives us:

m = (4 - 1) / (3 - 1) = 3 / 2

Now we have the slope, we can use the point-slope form to create an equation and then convert it to standard form. The point-slope form is:

y - y1 = m(x - x1)

Using (1, 1) as our point and a slope of 3/2:

y - 1 = 3/2(x - 1)

To transform to standard form, we'll multiply everything by 2 to avoid fractions, and then rearrange to get Ax + By = C:

2y - 2 = 3(x - 1)

2y - 2 = 3x - 3

Add 2 and subtract 3x from both sides:

-3x + 2y = -1

Answer 2

standard form is ax+by=c

first we use
y-y1=m(x-x1)
a point is (x1,y1)
the slope is m


the slope between the points (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
given
(1,1) and (3,4)
slope=(4-1)/(3-1)=3/2

a oint is (1,1) and slope is 3/2
y-1=3/2(x-1)
y-1=3/2x-3/2
solve for ax+by=c form, a is normally positive and a and b and c are whole numbers
times 2 both sides
2y-2=3x-3
minus 2y
-2=3x-2y-3
add 3
1=3x-2y
3x-2y=2