Find the slope-intercept form for the line passing through (5,7) and parallel to the line passing through (3,3) and (-9,1).

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Find the slope-intercept form for the line passing through  (5,7) and parallel to the line passing through  (3,3) and  (-9,1).

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Calculate Slope: First, we need to find the slope of the line that passes through the points (3,3) and (-9,1). The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).Find Parallel Line Slope: Using the points (3,3) and (-9,1), we calculate the slope as follows: m = (1 - 3) / (-9 - 3) m = (-2) / (-12) m = 1/6 The slope of the line passing through (3,3) and (-9,1) is 1/6.Determine Y-Intercept: Since the line we are looking for is parallel to the line passing through (3,3) and (-9,1), it will have the same slope. Therefore, the slope of our line is also 1/6.Substitute Values: Now, we need to find the y-intercept (b) of our line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We have a point (5,7) that lies on our line and the slope m = 1/6. We can substitute these values into the slope-intercept form to solve for b.Solve for b: Substituting the point (5,7) and the slope 1/6 into the equation y = mx + b, we get: 7 = (1/6)*5 + bCommon Denominator: To find b, we solve the equation: 7 = 5/6 + b To isolate b, we subtract 5/6 from both sides of the equation: 7 - 5/6 = bSubtract Numerators: To subtract 5/6 from 7, we need a common denominator. We can write 7 as 42/6: 42/6 - 5/6 = bCalculate Y-Intercept: Now we subtract the numerators: (42 - 5) / 6 = b 37 / 6 = b The y-intercept of our line is 37/6.Final Slope-Intercept Form: We now have both the slope and the y-intercept for our line. The slope-intercept form of the line is: y = (1/6)x + 37/6

Find the slope-intercept form for the line passing through $(5,7)$ and parallel to the line passing through $(3,3)$ and $(-9,1)$ .

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Find the slope-intercept form for the line passing through (5,7)(5,7)(5,7) and parallel to the line passing through (3,3)(3,3)(3,3) and (−9,1)(-9,1)(−9,1).

Find the slope-intercept form for the line passing through $(5,7)$ and parallel to the line passing through $(3,3)$ and $(-9,1)$ .