Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through(-3,-4) and parallel to the line whose equation is y = -6x + 1
Solution:-
The point-slope equation of a nonvertical line with slope m that passes through the point (x1,y1) is y- y1 = m(x – x1).
To use the point-slope form we need to find the slope of the line. If two nonvertical lines are parallel, then they have the same slope.
Thus, a line that is parallel to the line whose equation is y = -6x + 1 will have slpoe m = -6.
To use the point-slope equation we also need the coordinates of a point. We use the point given in the problem statement. Thus,(x1, y1) = (-3,-4).
Now we are ready to write the point-slope equation.
y –y1 = m(x-x1)
y – (-4) = -6 (x – (-3))
y + 4 = -6 (x+ 3 )
Therefore, the point-slope equation of the line is y +4 = -6 (x + 3).
Now we solve this equation for y and write an equivalent equation in slope-intercept form y = mx + b.
y + 4 = -6(x + 3)
y + 4 = -6x – 18
y = -6x – 22
Therefore, the slope-intercept form of the line’s equation is y = -6x – 22.