Write an equation of the line satisfying the given conditions
Parallel to the line y=-4x+3 and a y intercept of -5
Please help I am really confused
A line parallel to y=-4x+3 would be y=-4x-5. ( Parallel line have the same slope).
To find the equation of a line parallel to the line y = -4x + 3 and with a y-intercept of -5, we can use the fact that parallel lines have the same slope.
The given line has a slope of -4. So, we know that our parallel line will also have a slope of -4.
We can use the point-slope form of the equation of a line to find the equation. The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) is a point on the line, and m is the slope.
Since our parallel line has a y-intercept of -5, we know that one point on the line is (0, -5).
By substituting the values of the point and slope into the point-slope form, we get:
y - (-5) = -4(x - 0).
Simplifying the equation gives us:
y + 5 = -4x.
To put the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can rearrange the equation:
y + 5 = -4x,
y = -4x - 5.
Therefore, the equation of the line parallel to y = -4x + 3 and with a y-intercept of -5 is y = -4x - 5.