Final answer:
To find the equation of a line passing through two points (2,2) and (3,7), we can use the slope-intercept form of the equation: y = mx + b. First, find the slope (m) by taking the difference in y-coordinates divided by the difference in x-coordinates. Then, substitute one point and the slope into the equation to find the y-intercept (b). Finally, write the equation in the form y = mx + b.
Step-by-step explanation:
To find the equation of a line passing through two points, we can use the slope-intercept form of the equation: y = mx + b.
First, we need to find the slope (m) of the line. The slope is calculated by taking the difference in y-coordinates and dividing it by the difference in x-coordinates. For the given points (2,2) and (3,7), the slope is (7-2)/(3-2) = 5/1 = 5.
Next, we can substitute one of the points and the slope into the equation to find the y-intercept (b). Let's use the point (2,2). We have 2 = 5(2) + b. Solving for b, we get b = 2 - 10 = -8.
Therefore, the equation of the line is y = 5x - 8.