Answer:
y - 2 =7(x - 4)
Step-by-step explanation:
The point-slope form of a linear equation is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Point-slope form of a linear equation}}\\\\y-y_1=m(x-x_1)\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\textsf{ $(x_1,y_1)$ is a point on the line.}\end{array}}[/tex]
So, in the case of the linear equation y - 7 = 7(x - 3), its slope is m = 7, and a point on the line is (3, 7).
If two lines are parallel, they have the same slope. So, a line parallel to y - 7 = 7(x - 3) also has a slope of m = 7.
Given that the parallel line passes through point (4, 2), we can write the equation of this line by substituting its slope (m = 7) and the point (4, 2) into the point-slope form:
[tex]\Large\boxed{\boxed{y-2=7(x-4)}}[/tex]
Answer:
[tex] y - 2 = 7(x - 4) [/tex]
Step-by-step explanation:
The point-slope form of a linear equation is given by the formula:
[tex]\Large\boxed{\boxed{ y - y_1 = m(x - x_1) }}[/tex]
Where:
To find the equation of a line parallel to another line, we need to keep the slope the same.
Given the line:
[tex] y - 7 = 7(x - 3) [/tex]
which is in point-slope form, we can identify the slope.
The slope of this line is [tex] 7 [/tex], since it's the coefficient of [tex] (x - 3) [/tex].
Now, to find the equation of a line parallel to this line, we keep the slope the same and use the given point [tex] (4,2) [/tex].
The slope [tex] m [/tex] is [tex] 7 [/tex], and the point [tex] (x_1, y_1) [/tex] is [tex] (4,2) [/tex].
Substitute the values into the point-slope form:
[tex] y - 2 = 7(x - 4) [/tex]
The equation of the line parallel in point slope form is:
[tex] \Large\boxed{\boxed{ y - 2 = 7(x - 4) }}[/tex]
