Final answer:
To find the equation of a line with a given point (2,9) and a slope of 2, we use the point-slope form and rearrange it to the slope-intercept form y = mx + b, yielding y = 2x + 5.
Step-by-step explanation:
The student is asking for the equation of a line in slope-intercept form, which is expressed as y = mx + b. Given a point (2,9) on the line and a slope of 2, we can use the point-slope form to find the equation:
y - y1 = m(x - x1)
Where (x1, y1) is the point on the line and m is the slope. Substituting the given point and slope:
y - 9 = 2(x - 2)
Expanding and rearranging gives us the slope-intercept form:
y = 2x + 5
This equation represents a line that passes through the point (2,9) with a slope of 2.