Final answer:
To find the equation of the line that passes through the points (-1,-2) and (3,10), we calculate the slope (m) as 3 and the y-intercept (b) as 1, which leads to the equation y = 3x + 1.
Step-by-step explanation:
The equation that represents the line passing through the points (-1,-2) and (3,10) can be found using the formula for the slope, m, which is calculated by the difference in the y-values divided by the difference in the x-values (rise over run). After calculating the slope, we will use one of the points and the slope to find the y-intercept (b).
Firstly, calculate the slope using the two points:
- Let (x1,y1) be (-1,-2) and (x2,y2) be (3,10).
- The formula for the slope (m) is (y2 - y1) / (x2 - x1).
- Thus, m = (10 - (-2)) / (3 - (-1)) = 12 / 4 = 3.
The slope m is 3. Now find the y-intercept using the point-slope form y - y1 = m(x - x1) and one of the given points:
- Choose point (-1,-2) and plug it into the equation with our found slope. So, -2 - 3(-1) = -2 + 3 = 1.
- Therefore, the y-intercept b is 1.
The equation of the line is y = mx + b, which gives us y = 3x + 1; therefore, the correct equation is y = 3x + 1.