Final answer:
The equation of the line in slope-intercept form, given a slope of 2 and a point (-3,7), is y = 2x + 13.
Step-by-step explanation:
To write an equation of a line in slope-intercept form (y = mx + b), you need the slope (m) and the y-intercept (b). The question provides a slope of 2 and a point that the line passes through, which is (-3,7). We can use these to find the y-intercept.
Let's use the point-slope form of a linear equation to begin: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Plugging in the values we have:
y - 7 = 2(x + 3)
Now we distribute the slope on the right side:
y - 7 = 2x + 6
To find the y-intercept, we solve for y:
y = 2x + 6 + 7
y = 2x + 13
The equation of the line in slope-intercept form is y = 2x + 13.