An equation of a line through (-3, -6) which is perpendicular to the line y=-5 x +3 has slope: I know the slope is 1/5 having problem with y-intercept is
y intercept is when x is zero.
y=mx+b
-6=1/5 *-3 + b
solve for b.
or, just use the point-slope form of the line. You know the slope is 1/5 and it goes through (-3,-6). So,
y+6 = 1/5 (x+3)
You can massage that as you will.
To find the equation of a line that is perpendicular to another line, you need to determine the slope of the perpendicular line.
In this case, the given line has a slope of -5. The slope of a line perpendicular to this line can be found by taking the negative reciprocal of the given slope.
So, the slope of the perpendicular line would be the negative reciprocal of -5, which is 1/5.
Now, you have the slope (1/5) and one point (-3, -6) through which the line passes. To find the y-intercept of the line, you can use the point-slope form of the equation of a line, which is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point and m is the slope.
Substituting the values into the equation, you have:
y - (-6) = (1/5)(x - (-3))
Simplifying further:
y + 6 = (1/5)(x + 3)
To find the y-intercept, you can set x = 0 and solve for y:
y + 6 = (1/5)(0 + 3)
y + 6 = (1/5)(3)
y + 6 = 3/5
y = 3/5 - 6/5
y = -3/5
Therefore, the y-intercept is -3/5.
Putting it all together, the equation of the line that is perpendicular to y = -5x + 3 and passes through the point (-3, -6) is:
y = (1/5)x - 3/5