Q7: [tex]y = 2x+3[/tex]
Q8: [tex]y=-2x+5[/tex]
Q9: [tex]m = -\frac{A}{B}[/tex]
Step-by-step explanation:
Q7: Given equation of line is:
[tex]2x-y=1[/tex]
Converting into slope-intercept form
[tex]2x-y-1 = 1-1\\2x-y-1+y = 0+y\\y = 2x-1[/tex]
Comparing with the standard slope-intercept form
[tex]y = mx+b[/tex]
We get
m = 2
As the new line has same slope as given line
[tex]m_1 = 2[/tex]
Given
b = 3
The equation is given by:
[tex]y = m_1x+b[/tex]
Putting the values of slope and y-intercept
[tex]y = 2x+3[/tex]
Q8: Given equation of line is:
[tex]6x+3y = 12[/tex]
converting in slope-intercept form
[tex]3y = -6x+12[/tex]
Dividing both sides by 3
[tex]y = -2x+4[/tex]
The slope of line is: -2
The new line has same slope so,
m_1 = -2
Slope-intercept form of line is:
[tex]y = m_1x+b[/tex]
Putting the value of slope
[tex]y = -2x+b[/tex]
Putting the point (2,1) in the equation
[tex]1 = -2(2) +b\\1 = -4 +b\\b = 4+1\\b = 5[/tex]
So the equation is:
[tex]y=-2x+5[/tex]
Q9: Given equation is:
[tex]Ax+By = C[/tex]
subtracting Ax from both sides
[tex]Ax+By-Ax = C-Ax\\By = -Ax+C[/tex]
Dividing both sides by B
[tex]\frac{By}{B} = \frac{-Ax+C}{B}\\y = -\frac{A}{B}x + \frac{C}{B}[/tex]
As the equation is in slope-intercept form, the co-efficient of x is the slope of line
So the slope is:
[tex]m = -\frac{A}{B}[/tex]
Hence,
Q7: [tex]y = 2x+3[/tex]
Q8: [tex]y=-2x+5[/tex]
Q9: [tex]m = -\frac{A}{B}[/tex]
Keywords: Equation of line, slope
Learn more about equation of line at:
- brainly.com/question/9621364
- brainly.com/question/9539036
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