Answer:
y = 2x - 3.
Explanation:
The equation of a line can be written in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
We are given that the line has a slope of 2, so we can substitute m = 2 into the slope-intercept form to get:
y = 2x + b
We also know that the line contains the point (5,7). This means that the x-coordinate of the point is 5, and the y-coordinate of the point is 7. We can substitute these values into the equation to get:
7 = 2(5) + b
Simplifying the right-hand side gives:
7 = 10 + b
Subtracting 10 from both sides gives:
-3 = b
Therefore, the value of b is -3.
We now have both the slope and the y-intercept of the line. Substituting these values into the slope-intercept form gives the equation of the line:
y = 2x - 3
Therefore, the equation of the line that passes through the point (5,7) and has a slope of 2 is y = 2x - 3.