find the equation for the line with the given properties. Express in slope intercept. containing points P=(-5,1)and
(-3,0)
To find the equation of a line in slope-intercept form (y = mx + b), we need two pieces of information - the slope (m) and the y-intercept (b).
Step 1: Find the slope (m) using the given points, P=(-5,1) and (-3,0).
The slope (m) is given by the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-5, 1) and (x2, y2) = (-3, 0).
m = (0 - 1) / (-3 - (-5))
= -1 / (-3 + 5)
= -1 / 2
So, the slope (m) is -1/2.
Step 2: Substitute the slope (m) and one of the given points into the slope-intercept form to find the y-intercept (b).
Using point P=(-5,1):
1 = (-1/2)(-5) + b
1 = 5/2 + b
b = 1 - 5/2
b = 2/2 - 5/2
b = -3/2
So, the y-intercept (b) is -3/2.
Step 3: Write the equation using the slope (m) and y-intercept (b).
Therefore, the equation of the line in slope-intercept form is:
y = -1/2x - 3/2
To find the equation for a line using the slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
1. First, let's find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's assign (-5, 1) as (x₁, y₁) and (-3, 0) as (x₂, y₂).
m = (0 - 1) / (-3 - (-5))
m = -1 / (-3 + 5)
m = -1 / 2
So, the slope (m) is -1/2.
2. Next, we can use the slope-intercept form of a line, which is:
y = mx + b
We have the slope (m) as -1/2, and we need to find the y-intercept (b).
3. To find the y-intercept (b), we can substitute the coordinates of one of the given points into the equation and solve for b.
Let's use point P=(-5,1) as (x,y).
1 = (-1/2)(-5) + b
1 = 5/2 + b
To solve for b, subtract 5/2 from both sides:
1 - 5/2 = b
2/2 - 5/2 = b
-3/2 = b
So, the y-intercept (b) is -3/2.
4. Now we can substitute the values of m and b into the slope-intercept form equation:
y = mx + b
Therefore, the equation for the line, expressed in slope-intercept form, is:
y = -1/2x - 3/2
a line has a constant slope.
So, for any point (x,y), the slope of the line between (-5,1) and (x,y) is the same as the slope from (-5,1) and (-3,0). So,
(y-1)/(x+5) = (0-1)/(-3+5) = -1/2
y = -1/2 (x+5) + 1