Write an equation in slope-intercept form of the line satisfying the given conditions.
Through (negative 3,negative 7), perpendicular to negative 5 x minus 2 y equals 1
To find the equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.
First, we need to put the given equation in slope-intercept form (y = mx + b):
-5x - 2y = 1
-2y = 5x + 1
y = (-5/2)x - 1/2
So, the slope of the given line is -5/2. The negative reciprocal of -5/2 is 2/5.
Now, we can use the point-slope form of the equation of a line to find the equation of the line that passes through (-3, -7) with a slope of 2/5:
y - y1 = m(x - x1)
Substituting (-3, -7) and 2/5 for x1, y1, and m, respectively:
y - (-7) = (2/5)(x - (-3))
y + 7 = (2/5)(x + 3)
Expanding:
y + 7 = (2/5)x + (2/5)(3)
y + 7 = (2/5)x + 6/5
Rearranging the equation to slope-intercept form:
y = (2/5)x + 6/5 - 7
y = (2/5)x + 6/5 - 35/5
y = (2/5)x - 29/5
Hence, the equation of the line satisfying the given conditions is y = (2/5)x - 29/5 in slope-intercept form.