You observe that the line shown below passes through the point (0,4 )and has a slope of 1/2. You choose (x,y) as an arbitrary point on the line other than (0,4) and use the fact that the slope of a line is constant to write which equation?
you have the slope and the y-intercept ... y = 1/2 x + 4
All the answers plz
To write the equation of the line passing through the point (0,4) with a slope of 1/2, we can use the point-slope form of a line.
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.
Therefore, we have:
y - 4 = (1/2)(x - 0)
Simplifying this equation, we get:
y - 4 = (1/2)x
To have the equation in standard form, we can multiply through by 2 to eliminate the fraction:
2y - 8 = x
Rearranging the equation, we get:
x - 2y + 8 = 0
So, the equation of the line passing through (0,4) with a slope of 1/2 is:
x - 2y + 8 = 0
To write the equation of a line with a given slope and a point on the line, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m represents the slope and b represents the y-intercept.
In this case, we are given that the line passes through the point (0, 4) and has a slope of 1/2. Let's use this information to find the equation.
Given that the slope, m = 1/2, we can substitute this value into the equation:
y = (1/2)x + b
Now, we need to find the value of the y-intercept, b. To do this, we'll use the fact that the line passes through the point (0, 4). We can substitute the values of x = 0 and y = 4 into the equation:
4 = (1/2)(0) + b
Simplifying, we get:
4 = 0 + b
Therefore, b = 4.
Now that we have the value of b, we can substitute it back into the equation:
y = (1/2)x + 4
So, the equation of the line passing through the point (0, 4) and with a slope of 1/2 is:
y = (1/2)x + 4