Final answer:
The equation of the line passing through the points (-3, -4) and (7,26) is y = 3x + 5, which is found by first calculating the slope and then using it to find the y-intercept to write the equation in slope-intercept form.
Step-by-step explanation:
To find the equation of the line passing through the points (-3, -4) and (7,26), we first need to calculate the slope (m) using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Plugging in the values, we get:
m = (26 - (-4)) / (7 - (-3)) = 30 / 10 = 3.
Now that we have the slope, we use one of the two points to find the y-intercept (b). Using the point-slope form of a line (y - y1) = m(x - x1) and point (-3, -4), we have:
y + 4 = 3(x + 3)
y = 3x + 9 - 4
y = 3x + 5
Therefore, the equation in slope-intercept form is y = 3x + 5, which is option B.