A line with slope 3 passes through the point (0; 10). What is the y-coordinate of the point on the
line with x-coordinate 2?
the slope is 3, so if x changes by 2, y changes by 6.
To find the y-coordinate of the point on the line with x-coordinate 2, we need to use the slope-intercept form of a line, which is y = mx + b. In this equation, m represents the slope of the line, and b represents the y-intercept.
Given that the line has a slope of 3 and passes through the point (0, 10), we can substitute these values into the equation to find the value of b. Let's plug in the values:
10 = 3(0) + b
Since any number multiplied by 0 is 0, the equation simplifies to:
10 = b
Therefore, the y-intercept of the line is 10.
Now that we know the slope (m = 3) and the y-intercept (b = 10), we can use the slope-intercept form of the line equation to find the y-coordinate of the point on the line with x-coordinate 2. Let's plug in the values:
y = 3x + 10
Substituting x = 2:
y = 3(2) + 10
y = 6 + 10
y = 16
Therefore, the y-coordinate of the point on the line with x-coordinate 2 is 16.
To find the y-coordinate of the point on the line with x-coordinate 2, we need to use the point-slope formula for a line.
Given that the line has a slope of 3 and passes through the point (0, 10), we can write the equation of the line as:
y - y1 = m(x - x1)
Substituting the values for the slope (m = 3) and the coordinates (x1 = 0, y1 = 10), we have:
y - 10 = 3(x - 0)
Simplifying the equation further, we have:
y - 10 = 3x
Now, substitute the x-coordinate 2 into the equation:
y - 10 = 3(2)
Simplify the right side:
y - 10 = 6
Finally, solve for y:
y = 6 + 10
y = 16
Therefore, the y-coordinate of the point on the line with an x-coordinate of 2 is 16.