Answer :
Parallel lines have the same slope.
We have the general form of line. Transform to the slope-intercept form:
[tex]y=mx+b[/tex]
m - slope, b - y-intercept
[tex]7y+2x-10=0[/tex] subtract 2x from both sides
[tex]7y-10=-2x[/tex] add 10 to both sides
[tex]7y=-2x+10[/tex] divide both sides by 7
[tex]y=-\dfrac{2}{7}x+\dfrac{10}{7}\to m=-\dfrac{2}{7}[/tex]
Therefore we have: [tex]y=-\dfrac{2}{7}x+b[/tex].
The line passes through the point (2, 2). Substitute the coordinates of the point to the equation of a line:
[tex]2=-\dfrac{2}{7}(2)+b[/tex]
[tex]2=-\dfrac{4}{7}+b[/tex] add [tex]\dfrac{4}{7}[/tex] to both sides
[tex]2\dfrac{4}{7}=b[/tex]
[tex]y=-\dfrac{2}{7}x+2\dfrac{4}{7}[/tex]
[tex]y=-\dfrac{2}{7}x+\dfrac{18}{7}[/tex] multiply both sides by 7
[tex]7y=-2x+18[/tex] subtract 7y from both sides
[tex]0=-2x-7y+18[/tex] change the signs
[tex]2x+7y-18=0[/tex]
Answer:
[tex]y=-\dfrac{2}{7}x+\dfrac{18}{7}[/tex] slope-intercept form
[tex]2x+7y-18=0[/tex] general form