Question

Write an equation in standard form of the line that passes through the given points (2,5) and (1,1)

Answer 1

To write the equation of a line that passes through the given points (2,5) and (1,1), you can use the slope-intercept form of the equation of a line, which is given by the formula y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To find the slope of the line, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the coordinates of the given points, you get:
m = (1 - 5)/(2 - 1) = -4/1 = -4

To find the y-intercept, you can plug the slope and one of the points into the slope-intercept form of the equation. For example, using the point (2,5), you get:
5 = -4 * 2 + b
b = 5 + 8
b = 13

Thus, the equation of the line in standard form is:
y = -4x + 13

This equation represents the line that passes through the given points (2,5) and (1,1).

Answer 2

The equation of the line passing through the points (2,5) and (1,1) is 4x - y = 3 in standard form.

The standard form of the equation of a line is given by:

Ax + By = C

To find the equation of the line passing through the points (2,5) and (1,1), we can use the point-slope form of the equation:

(y - y₁)/(x - x₁) = m

where m is the slope of the line and (x₁, y₁) is a point on the line. Let's calculate the slope first:

m = (y₂ - y₁)/(x₂ - x₁)

Using the points (2,5) and (1,1):

m = (1 - 5)/(1 - 2) = (-4)/(-1) = 4

Now that we have the slope (m = 4), we can use one of the given points to write the point-slope form. Let's use the point (2,5):

(y - 5)/(x - 2) = 4

Multiply both sides by (x - 2) to get rid of the fraction:

y - 5 = 4(x - 2)

Distribute 4 on the right side:

y - 5 = 4x - 8

Add 5 to both sides:

y = 4x - 3

Now, let's write this equation in standard form:

4x - y = 3

So, the equation of the line in standard form is 4x - y = 3.