Write an equation that represents the line that passes through the points (5,4) and (-5,0).
I got y=2/5 * x
is that right?
you have the slope right, lets check y intercept
y=2/5 x + b
putting in the point 5,4
4=2/5 5 + b
4=10+b
b=-6
y=2/5 * x -6
thanks
To determine whether your equation is correct, we can use the slope-intercept form of a linear equation:
y = mx + b
where:
m represents the slope of the line
b represents the y-intercept of the line
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given coordinates (5,4) and (-5,0) into the formula:
m = (0 - 4) / (-5 - 5) = -4 / -10 = 2/5
So, the correct equation should be:
y = (2/5)x + b
Now, we can substitute one of the given points into the equation, (5,4), to find the value of b:
4 = (2/5)(5) + b
4 = 2 + b
b = 4 - 2
b = 2
Therefore, the equation of the line passing through the points (5,4) and (-5,0) is:
y = (2/5)x + 2
Thus, your equation y = 2/5x is incorrect. The correct equation is y = (2/5)x + 2.
To find the equation of a line that passes through two points, you can use the point-slope form of a linear equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Let's find the slope using the given points (5, 4) and (-5, 0). The slope is given by the formula m = (y2 - y1)/(x2 - x1). Plugging the coordinates into the formula, we get:
m = (0 - 4)/(-5 - 5) = -4/-10 = 2/5
So the slope of the line is 2/5. Now, let's choose one of the points, say (5, 4), to plug into the point-slope form.
Using the point (5, 4) and the slope 2/5, the equation becomes:
y - 4 = (2/5)(x - 5)
Now, simplify the equation to put it in the standard form, y = mx + b:
y - 4 = (2/5)x - 2
y = (2/5)x - 2 + 4
y = (2/5)x + 2
Therefore, the equation representing the line passing through the points (5, 4) and (-5, 0) is y = (2/5)x + 2.
Your answer of y = (2/5)x is close, but it is missing the constant term, which is 2 in this case.