Module 11 Assessment Readiness
Sign In
Write the equation in slope-intercept form.
Write the equation in slope-intercept form.
Write the equation in slope-intercept form.
Yes.
No.
Yes.
We are given a graph representing a system of linear equations, and need to determine whether each of the given equations is part of the system. To investigate this, we will follow a three step process.
The slope-intercept form of a line is y=mx+b, where m is the slope and b the y-intercept.
To write the equation 3x+y=5 in slope-intercept form, we will isolate the y-variable.
3x+y=5 ⇔ y=- 3x+5
We can see in the graph that the slope of the blue line is 4 and the y-intercept is - 2. y=4x-2 Let's now find the equation of the red line.
We can see in the graph that the slope of the red line is - 3 and the y-intercept is 5. y=- 3x+5 The given equation, when written in slope-intercept form, matches the second equation from the system shown in the graph. Therefore, it is part of the system.
To write the equation 2x+3y=8 in slope-intercept form, we will isolate the y-variable.
LHS-2x=RHS-2x
.LHS /3.=.RHS /3.
Write as a sum of fractions
a* b/c=a/c* b
Put minus sign in front of fraction
Therefore, the slope-intercept form of the second equation is as follows. y=- 2/3x+8/3 Looking back to Part A, we can tell that this equation does not match either of the equations of the graphed lines. Therefore, it is not part of the system.
To write the equation - 8x+2y=- 4 using the slope-intercept form, we need to isolate the y-variable.
LHS+8x=RHS+8x
.LHS /2.=.RHS /2.
Write as a sum of fractions
a* b/c=a/c* b
Calculate quotient
Therefore, the slope-intercept form of the third equation is as follows. y=4x-2 Once more, referring back to Part A. We can see that this equation matches that of the first line graphed in the system. Therefore, it is part of the system.