A line’s equation is given in point-slope form:
y-17=3 (x-4)
This line’s slope is :
A point on this line that is apparent from the given equation is:
There are infinite points that can work. What are the options?
The "apparent" point is (4,17)
among the "many" others.
To find the slope of the line, we can observe the given equation in point-slope form: y - 17 = 3(x - 4).
The equation is in the form y - y₁ = m(x - x₁), where m represents the slope of the line.
Comparing this with the given equation, we can see that the slope is 3.
Therefore, the slope of the line is 3.
Regarding a point on this line that is apparent from the given equation, we can identify the point (4, 17).
This is apparent because the equation is in point-slope form, which indicates that the line passes through the given point.
Therefore, the point (4, 17) is apparent from the given equation.
To find the slope of a line given in point-slope form, we need to convert the equation to slope-intercept form, which is in the following form: y = mx + b, where m represents the slope of the line.
In the given equation, y - 17 = 3(x - 4), we can distribute the 3 on the right side:
y - 17 = 3x - 12
Next, we can isolate y by adding 17 to both sides of the equation:
y = 3x - 12 + 17
Simplifying this further:
y = 3x + 5
From the equation y = 3x + 5, we can see that the slope, m, is 3. Therefore, the slope of the line described by the given equation is 3.
Now, let's move on to finding a point on this line that is apparent from the given equation. In the equation, we can observe that the x-coordinate is 4, as it is given as (x - 4). By substituting x = 4 into the equation, we can find the corresponding y-coordinate:
y = 3(4) + 5
y = 12 + 5
y = 17
Hence, the point on this line that is apparent from the given equation is (4, 17).