Write an equation of the line satisfying the given conditions in stand form. Ax+By=C
How would you do this?
m=2 and contains (-3,1)
(-3,1)=(x1,y1)
y-y1=m(x-x1)
find the equation of the givin pair of points and write in slop intercept form.
(1/3,-5) (13/3,-8)
To write the equation of a line in standard form (Ax + By = C), you need two pieces of information: the slope of the line (m) and a point on the line (x, y).
In this case, you are given that the slope (m) is 2, and the line passes through the point (-3,1).
Step 1: Determine the slope-intercept form of the equation (y = mx + b), where m is the slope and b is the y-intercept.
The slope-intercept form is y = 2x + b.
Step 2: Use the given point (-3,1) to find the value of b (the y-intercept).
Plug in the x-coordinate (-3) and y-coordinate (1) into the slope-intercept form equation, and solve for b:
1 = 2(-3) + b,
1 = -6 + b,
b = 7.
Step 3: Substitute the values of m and b into the slope-intercept form equation to get the final equation.
The equation becomes: y = 2x + 7.
Step 4: Convert the equation to standard form (Ax + By = C).
To convert the equation to standard form, you need to get rid of the fraction and rearrange the equation.
Start by multiplying the entire equation by the common denominator of the coefficients of x and y, which is 2:
2y = 4x + 14.
Next, move all the variables to one side and the constant term to the other side:
-4x + 2y = 14.
Finally, rearrange the equation so that the coefficient of x (A) is positive:
4x - 2y = -14.
So, the equation of the line in standard form that satisfies the given conditions is 4x - 2y = -14.