How do you write the standard form of the equation of the line passing through the points M(-4,-2) and N(4,7)?
How do you find the slope-intercept form of the equation of the line passing through the points P(2,-9) and Q(3,-7)?
standard form is
y=mx+b
where m is slope, x is x value in (x,y) and b is the y intercept.
Find slope by using y2-y1/x2-x1
To write the standard form of the equation of a line passing through two points, you can use the formula:
Ax + By = C
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
For the first question, using the points M(-4, -2) and N(4, 7), the slope (m) is:
m = (7 - (-2)) / (4 - (-4))
m = 9 / 8
Step 2: Choose one point (M or N) and substitute its coordinates into the equation Ax + By = C to find the value of C. Let's choose point M(-4, -2):
A(-4) + B(-2) = C
-4A - 2B = C
Step 3: Substitute the slope (m) into the equation (A and B are variables):
-4A - 2B = C (Equation 1)
B = m(A) (Equation 2)
Step 4: Eliminate B by substituting Equation 2 into Equation 1:
-4A - 2(mA) = C
-4A - 2mA = C
Step 5: Simplify the equation:
-4A - 2mA = C
-4A - 2mA = C
-4 - 2m = C
Step 6: Write the standard form of the equation:
-4x - 2y = C
So, the standard form of the equation of the line passing through the points M(-4,-2) and N(4,7) is:
-4x - 2y = C.
For the second question, the process is similar. Let's use points P(2,-9) and Q(3,-7):
Step 1: Find the slope (m):
m = (-7 - (-9)) / (3 - 2)
m = 2 / 1
m = 2
Step 2: Choose one point (P or Q). Let's use point P(2,-9):
A(2) + B(-9) = C
2A - 9B = C
Step 3: Substitute the slope (m):
2A - 9B = C
B = 2A
Step 4: Eliminate B:
2A - 9(2A) = C
2A - 18A = C
-16A = C
Step 5: Write the equation in standard form:
-16x - y = C
So, the standard form of the equation of the line passing through the points P(2,-9) and Q(3,-7) is:
-16x - y = C.