Find the slope intercept equation of the line with the following properties: Parallel to the line 5x+2y=1; containing points (-5,4)
5x+2y=1
2 y = -5 x + 1
y = (-5/2) x + 1/2
so m, the slope = -5/2
y = (-5/2) x + b
4 = (-5/2)(-5) + b
8/2 = 25/2 + b
b = -17/2
so
y = (-5/2)x - 17/2
2 y + 5 x = -17
To find the slope-intercept equation of a line, we need two pieces of information: the slope (m) and the y-intercept (b).
First, let's find the slope of the given line, 5x + 2y = 1. To do this, we rearrange the equation to be in the standard form y = mx + b, where m is the slope and b is the y-intercept.
Start by isolating y on one side of the equation:
5x + 2y = 1
2y = -5x + 1
y = (-5/2)x + 1/2
Comparing this equation to y = mx + b, we see that the slope (m) is -5/2.
Since the line we are looking for is parallel to the given line, it will have the same slope, which means m = -5/2.
Now that we know the slope (m), we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
In this case, the given point is (-5, 4). So, plugging in the values, we have:
y - 4 = (-5/2)(x - (-5))
y - 4 = (-5/2)(x + 5)
Next, simplify the equation:
y - 4 = (-5/2)(x + 5)
y - 4 = (-5/2)x - 25/2
Finally, rearrange the equation to the slope-intercept form, y = mx + b, by isolating y:
y = (-5/2)x - 25/2 + 4
y = (-5/2)x - 25/2 + 8/2
y = (-5/2)x - 17/2
Therefore, the slope-intercept equation of the line parallel to 5x + 2y = 1 and containing the point (-5, 4) is y = (-5/2)x - 17/2.