What is the equation of the line that passes through points (4, -2) and (0, 3)?
To find the equation of a line that passes through two given points, you can use the slope-intercept form equation, which is: y = mx + b, where m is the slope of the line and b is the y-intercept.
1. First, find the slope (m) of the line using the two given points (x1, y1) and (x2, y2). The slope of a line is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values of the given points, we get:
m = (3 - (-2)) / (0 - 4)
= 5 / (-4)
= -5/4
2. Now that we have the slope (m), we can use one of the given points (let's use (4, -2)) to find the y-intercept (b) of the line.
Plug in the coordinates of the point (4, -2) into the slope-intercept form equation and solve for b:
-2 = (-5/4)(4) + b
-2 = -5 + b
b = -2 + 5
b = 3
3. We have the slope (m = -5/4) and the y-intercept (b = 3), so we can construct the equation of the line:
y = (-5/4)x + 3
Therefore, the equation of the line that passes through the points (4, -2) and (0, 3) is y = (-5/4)x + 3.
To find the equation of the line that passes through two points, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the coordinates of one of the points, and m represents the slope of the line.
First, let's find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given the points (4, -2) and (0, 3), we have:
m = (3 - (-2)) / (0 - 4)
= 5 / (-4)
= -5/4
Now that we have the slope (m = -5/4), we can pick any of the two points to substitute into the point-slope form. Let's use the first point (4, -2):
y - (-2) = -5/4(x - 4)
Simplifying:
y + 2 = -5/4(x - 4)
Multiply both sides by 4 to eliminate the fraction:
4(y + 2) = -5(x - 4)
Expanding:
4y + 8 = -5x + 20
Rearranging the terms to get the standard form:
5x + 4y = 20 - 8
5x + 4y = 12
So, the equation of the line passing through the points (4, -2) and (0, 3) is 5x + 4y = 12.