If (8, 7) are the coordinates of a point on a line that has slope –3, what is the y-coordinate of the point on the line at which x=1
first find the equation:
with slope of -3 and the point(8,7) on it, using
y = mx + b
7 = -3(8) + b
31
y = -3x + 31
when x = 1
y = -3(1) + 31 = 28
To find the y-coordinate of the point on the line when x = 1, we will use the point-slope form of a linear equation.
First, let's recall the point-slope form of a linear equation, which is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line, m is the slope of the line.
In this case, the given point on the line is (8, 7), and the slope of the line is -3. So the equation becomes:
y - 7 = -3(x - 8)
Now, we substitute x = 1 into the equation to find the y-coordinate of the point on the line:
y - 7 = -3(1 - 8)
Simplifying:
y - 7 = -3(-7)
y - 7 = 21
Finally, add 7 to both sides of the equation to isolate y:
y = 21 + 7
y = 28
Therefore, the y-coordinate of the point on the line when x = 1 is 28.