Slope equal to 2 and passing through (-5,1)
Write the equation of a line in standard form
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slope intercept form of equation for line:
y = mx + b
m = 2, x = -5, y = 1
1 = 2(-5) + b
1 = -10 + b
b = 11
y = 2x + 11 equation(1)
standard form for equation of line is:
Ax + By = C, so we rearrange the equation (1)
2x - y = -11
Standard Form of a line is:
Ax + By = C where A is a positive integer, and B, and C are integers.
So we have a few conditions we must meet.
We can plug those numbers into our slope-intercept equation (Y= M * X + B) where M is the slope and B is the Y-intercept.
We will first use the points to solve for B, and then convert that to Standard Form:
Solve for B:
1 = 2 * (-5) + B
1 - ( 2 * (-5) ) = B
1 + 10 = B = 11
Convert to Standard Form:
Y = 2 * X + 11 ; Subtract Y from both sides to keep A positive
0 = 2 * X - Y + 11; Subtract 11 from both sides
-11 = 2X - Y
2X - Y = -11
A = 2
B = -1
C = -11
-11 = 2 (-5) - (1) = -11
The standard equation of a line with a slope m and an intercept b is given by the equation
y= mx + b
However when given only the slope and a point of interception not on the y-axis, we best use the slope intercept formula which is given by;
where (x1,y1) is the point of intersection and m is the slope. We will substitute and solve for y.
y-1 = 2(x-(-5))
y-1 = 2x+10
y = 2x+ 11
Therefore the standard form for the equation in question is