Identify the correct slope and y intercept of the equation 6x – 3y = 12

2 answers:

8 0

Y = mx + b
m = slope
b = y intercept.

6x - 3y = 12
-3y = -6x + 12
-3y/-3 = -6x/-3 + 12/-3
y = 2x - 4
m = slope = 2
b = y intercept = -4

y = -x + 6
m = -1 ; b = 6

(-4,-2)
Since it is perpendicular to y = -x + 6, the slope of (-4,-2) is the opposite reciprocal of the -1.

m = +1

-2 = 1(-4) + b
-2 = -4 + b
b = -2 + 4
b = 2

y = x + 2 is the equation of the line passing through the point (-4,-2)

Zina [86]3 years ago

5 0

Equation of a line is given by y = mx + c; where m is the slope and c is the y-intercept.
For line 6x - 3y = 12
3y = 6x - 12
y = 6/3 x - 12/3
y = 2x - 4

Therefore, slope is 2.

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3 years ago

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{2x+2y=2,2(x+y)=10}A. single solution B. no solution C. infinite solutions

mixer [17]

To find the number of solutions of a system of linear equations you need to identify the slope (m) in each equation:

$y=mx+b$

-If the slope is the same in both lines the system has no solution

-If the slope is different in the lines the system has one solution

-If the equation are the same (incluided the value of b) the system has infinitely many solutions

You have the next equations:

$\begin{gathered} 2x+2y=2 \\ 2(x+y)=10 \end{gathered}$

Write the equations in slope-intercept form y=mx+b (solve for y).

First equation:

$\begin{gathered} 2y=-2x+2 \\ y=-\frac{2}{2}x+\frac{2}{2} \\ \\ y=-x+1 \end{gathered}$

Second equation:

$\begin{gathered} 2x+2y=10 \\ 2y=-2x+10 \\ y=-\frac{2}{2}x+\frac{10}{2} \\ \\ y=-x+5 \end{gathered}$ As the equations have the same slope m = -1, the system has no solution (the line doesn't cross each other)