Final answer:
To find the equation in slope-intercept form, we need to calculate the slope using the formula (y2 - y1) / (x2 - x1) and then use the point-slope form to write the equation. The equation of the line passing through (1,4) and (3,10) is y = 3x + 1.
Step-by-step explanation:
To write the equation in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The formula for finding the slope is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. So, the slope is (10 - 4) / (3 - 1) = 6 / 2 = 3. Now, we can use the point-slope form y - y1 = m(x - x1) to write the equation. Substituting (1,4) as (x1, y1) and m = 3, we get y - 4 = 3(x - 1). Simplifying this equation, we get y = 3x - 3 + 4, which can be written as y = 3x + 1. Hence, the equation in slope-intercept form of the line that passes through (1,4) and (3,10) is y = 3x + 1.
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