Find the equation of the line
With a slope of (-1/3) that goes through the point (2, -4)
With a slope of 3 that goes through the point (-5, -1)
i need help with them??
see the technique I used on the other post you did
To find the equation of a line, we need to use the slope-intercept form of a line equation, which is given by:
y = mx + b
where "m" represents the slope of the line, and "b" represents the y-intercept.
Let's start with the first question: Find the equation of the line with a slope of (-1/3) that goes through the point (2, -4).
Step 1: Substitute the given values into the equation.
We have the slope m = -1/3 and the point (2, -4). Substituting these values, we get:
-4 = (-1/3)(2) + b
Step 2: Solve for the y-intercept (b).
Multiply -1/3 by 2:
-4 = -2/3 + b
To undo the subtraction of -2/3 from -4, we add -2/3 to both sides:
-4 + 2/3 = b
To add -4 and 2/3, we need to convert -4 into a fraction with a denominator of 3 (since 3 is the denominator for -1/3). Thus, -4 can be written as -12/3:
-12/3 + 2/3 = b
-10/3 = b
So, the y-intercept (b) is -10/3.
Step 3: Substitute the slope and y-intercept into the equation.
Now that we have the values of m = -1/3 and b = -10/3, we can substitute them into the slope-intercept form equation y = mx + b:
y = (-1/3)x - 10/3
Therefore, the equation of the line with a slope of -1/3 that goes through the point (2, -4) is y = (-1/3)x - 10/3.
Now let's move on to the second question: Find the equation of the line with a slope of 3 that goes through the point (-5, -1).
Step 1: Substitute the given values into the equation.
We have the slope m = 3 and the point (-5, -1). Substituting these values, we get:
-1 = 3(-5) + b
Step 2: Solve for the y-intercept (b).
Multiply 3 by -5:
-1 = -15 + b
To undo the subtraction of -15 from -1, we add -15 to both sides:
-1 + 15 = b
14 = b
So, the y-intercept (b) is 14.
Step 3: Substitute the slope and y-intercept into the equation.
Now that we have the values of m = 3 and b = 14, we can substitute them into the slope-intercept form equation y = mx + b:
y = 3x + 14
Therefore, the equation of the line with a slope of 3 that goes through the point (-5, -1) is y = 3x + 14.