Final answer:
To find a linear equation that passes through two given points, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. By finding the slope and substituting one of the points, we can determine the equation of the line.
Step-by-step explanation:
To find a linear equation that passes through the points (-3,7) and (1,19), we can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept. First, we need to find the slope:
slope (m) = (y2 - y1) / (x2 - x1) = (19 - 7) / (1 - (-3)) = 12 / 4 = 3
Now, we can substitute one of the points and the slope into the equation: y - y1 = m(x - x1)
Using the point (1,19): y - 19 = 3(x - 1)
Simplifying the equation gives us: y - 19 = 3x - 3
Finally, rearranging the equation to the standard form gives us: y = 3x + 16