Question

which equation describes this line (1,13) (-2,4)

Answer 1

using point slope

Answer 2

The equation that describes the line passing through the points (1, 13) and (-2, 4) can be found using the slope-intercept form of a linear equation, y = mx + b.
First, let's find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (1, 13) and (x2, y2) = (-2, 4).
m = (4 - 13) / (-2 - 1) = -9 / -3 = 3.
Now, substitute the slope (m) and one of the given points (x1, y1) into the slope-intercept form (y = mx + b) to find the y-intercept (b).
Using the point (1, 13):
13 = 3(1) + b
13 = 3 + b
b = 13 - 3
b = 10.
So, the equation of the line passing through the points (1, 13) and (-2, 4) is y = 3x + 10.

Answer 3

To find the equation of the line using the point-slope form, we can use the formula: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope.

Let's use the point (1, 13) as (x1, y1) and the slope m, which we found earlier to be 3.

Substituting the values into the point-slope form:
y - 13 = 3(x - 1)

Expanding the equation:
y - 13 = 3x - 3

Rearranging the equation to slope-intercept form:
y = 3x - 3 + 13
y = 3x + 10

Therefore, the equation that describes the line passing through the points (1, 13) and (-2, 4) is y = 3x + 10.