Answer:
Pat a) The graph in the attached figure
Part b) [tex]y=(4/3)x-5[/tex]
The slope is [tex]m=(4/3)[/tex]
The y-coordinate of the y-intercept is [tex]b=-5[/tex]
Step-by-step explanation:
Part a) Which line represents the linear equation [tex]-3y=15-4x[/tex]?
To graph the linear equation find the intercepts
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]-3y=15-4(0)[/tex]
[tex]-3y=15[/tex]
[tex]y=-5[/tex]
The y-intercept is the point [tex](0,-5)[/tex]
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
[tex]-3(0)=15-4x[/tex]
[tex]4x=15[/tex]
[tex]x=15/4=3.75[/tex]
The x-intercept is the point [tex](3.75,0)[/tex]
Plot the intercepts to graph the linear equation
see the attached figure
Part b) Rewritten in slope-intercept form
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
we have
[tex]-3y=15-4x[/tex]
convert to slope intercept form
isolate the variable y
[tex]3y=4x-15[/tex]
[tex]y=(4/3)x-5[/tex]
The slope is [tex]m=(4/3)[/tex]
The y-coordinate of the y-intercept is [tex]b=-5[/tex]
