Find an equation of the line (in slope-intercept form) that passes through the point (7,5) and is perpendicular to the line 7x + 10y - 17 = 0
y=?
First put the perpendicular line equation into y=mx+b form. Your first step should be to subtract the 10y from both sides.
Then using the y = mx + b equation, you know the slope of the parallel line. Your line is perpendicular to the m value in the new equation. To find the slope use: -1/m. That number will be your m value in your equation.
Finally plug your numbers into the basic starter equation:
y-(yval)=m(x-(xval))
your yval and xval numbers are from the point the line passes through
To find the equation of a line that is perpendicular to the given line, we need to first find the slope of the given line and then determine the negative reciprocal of that slope.
The given line is in the form of Ax + By + C = 0, where A = 7, B = 10, and C = -17. To find the slope of the given line, we rearrange the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Starting with the given equation:
7x + 10y - 17 = 0
Rearranging the equation to slope-intercept form:
10y = -7x + 17
y = -(7/10)x + 17/10
From the slope-intercept form, we see that the slope (m) of the given line is -7/10.
To find the slope of the line perpendicular to the given line, we take the negative reciprocal of the slope. The negative reciprocal of -7/10 is 10/7.
So, the slope of the line perpendicular to the given line is 10/7.
Now, we can find the equation of the line that passes through the point (7,5) using the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Using the point (7,5) and the slope 10/7, we have:
y - 5 = (10/7)(x - 7)
To get the equation in slope-intercept form, we can simplify this equation further by distributing the (10/7) and rearranging it:
y - 5 = (10/7)x - 10
y = (10/7)x - 10 + 5
y = (10/7)x - 5
Therefore, the equation of the line that passes through the point (7,5) and is perpendicular to the line 7x + 10y - 17 = 0 is y = (10/7)x - 5.