Final answer:
To find the equation of the line, calculate the slope (m), which is 2/5, using the two given points, then use the slope with one of the points to find the y-intercept (b=9/5). The equation of the line, in slope-intercept form, is y = (2/5)x + 9/5.
Step-by-step explanation:
To find an equation of the line that passes through the points (-2, 1) and (3, 3), we need to calculate the slope (m) of the line and use one of the points to write the equation in point-slope form, standard form, or slope-intercept form.
First, we find the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (3 - 1) / (3 - (-2)) = 2 / 5.
Now, using the slope-intercept form (y = mx + b) and one of the points, say (-2, 1), we can find the y-intercept (b). We substitute for x, y, and m to get: 1 = (2/5)(-2) + b, which simplifies to b = 1 + 4/5 = 9/5.
Finally, the equation of the line in slope-intercept form is y = (2/5)x + 9/5.