Answer
$y=1.75(x)-4.2$
Work Step by Step
RECALL:
(1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$ is the y-coordinate of the line's y-intercept.
(3) Parallel lines have equal slopes.
(4) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
Write $4x+7y=1$ in slope-intercept form:
$4x+7y=1
\\7y=1-4x
\\7y=-4x+1
\\\frac{7y}{7}=\frac{-4x+1}{7}
\\y=-\frac{4}{7}x+\frac{1}{7}$
This means the equation $4x+7y=1$ is equivalent to $y=-\frac{4}{7}x+\frac{1}{7}$.
The line is perpendicular to $y=-\frac{4}{7}x+\frac{1}{7}$. Since the slope of this line is $-\frac{4}{7}$, then the slope of the line perpendicular to it is the negative reciprocal of $-\frac{4}{7}$, which is $\frac{7}{4}=1.75$.
Using the given point on the line $(0, -4.2)$ (which is the y-intercept) and the slope $1.75$, the slope-intercept form of the line's equation is:
$y=1.75x+(-4.2)
\\y=1.75x-4.2$
