Answer:
The equation of line parallel to y = 2x + 7 and passes through (-1, 3) is: [tex]y = 2x+5[/tex]
Step-by-step explanation:
Given equation of line is:
y = 2x + 7
The general form of equation in slope-intercept form is:
[tex]y=mx+b[/tex]
Here m is the slope and b is the y-intercept
Comparing the equations, we get
m = 2
Let m_1 be the slope of line parallel to given line
[tex]m_1 = m\\m_1 = 2[/tex]
The equation of line parallel to given line will be:
[tex]y=m_1x+b[/tex]
Putting the value of slope
[tex]y = 2x+b[/tex]
To find the y-intercept, putting (-1,3) in the equation
[tex]3 = 2(-1)+b\\3 = -2+b\\3+2 = b\\b = 5[/tex]
The equation is:
[tex]y = 2x+5[/tex]
Hence,
The equation of line parallel to y = 2x + 7 and passes through (-1, 3) is: [tex]y = 2x+5[/tex]
