what is the equation of the line that passes through the point (7,4) and parallel to the line 2x-7y=-6

Answer 1

The equation for a line is given by a slope (m) and a single point on the line (x₁,y₁). We can also define a line given two points on the line but that's not what we are doing in this case. The easiest form of a line to use in this case is the point-slope form ( y-y₁=m(x-x₁) ). We will fill in the missing information into this equation. We are given a point on the line (7,4). That will be our x₁ and y₁. We find the slope m by remembering that parallel lines have the same slope. So we only need to find the slope of the line 2x - 7y = -6. Rewrite that given line in slope-intercept form ( y = mx + b ) to see what it's slope is. (hint: move the 2x to the right-hand side of the equation and divide both sides by -7 to isolate y and the equation will be in slope-intercept form)