Write an equation that is parallel to y=1/4-7 and goes through the point (4,-5)
y=mx+b
-5=1/4(4)+b
-5=1+b
Subtract 1 from both sides: -6=b
Answer: y=1/4x-6
The most useful form of straight-line equations is the "slope-intercept" form:
y = mx + b
m is the slope and "b" gives the
y-intercept.
The other format for straight-line equations is called the "point-slope" form. For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this formula:
y-y1= m(x β x1)
m is the slope and "b" gives the
y-intercept.
Parallel lines have same slope.
In this case:
m=1/4
x1=4
y1= -5
y-y1= m(x β x1)
y-(-5)= 1/4(x-4)
y+5=(1/4)x-(4/4)
y+5=(1/4)x-1
y=(1/4)x-1-5
y=(1/4)x-6
To find an equation that is parallel to the given equation y = (1/4)x - 7 and goes through the point (4, -5), we need to consider the fact that parallel lines have the same slope.
The given equation is already in slope-intercept form (y = mx + b), where m represents the slope of the line. In this case, the slope is 1/4.
To find a parallel line, we can start by using the slope-intercept form again:
y = mx + b
Since the new line is parallel to the given line, it will have the same slope, which is 1/4. Therefore, our new equation becomes:
y = (1/4)x + b
To determine the value of b, we can substitute the coordinates (4, -5) into the equation and solve for b:
-5 = (1/4)(4) + b
Simplifying:
-5 = 1 + b
To isolate b, we subtract 1 from both sides:
b = -5 - 1
b = -6
Therefore, the equation of the line that is parallel to y = (1/4)x - 7 and goes through the point (4, -5) is:
y = (1/4)x - 6