Question

(2,-8),(6,10) Write an equation in standard form for the line that passes through the given points, and the work

Answer 1

To find the standard form of the equation for the line that passes through (2, -8) and (6, 10), calculate the slope, use point-slope form, and rearrange into standard form, resulting in 9x - 2y - 34 = 0.

Step-by-step explanation:

To write an equation of a line in standard form that passes through the points (2, -8) and (6, 10), we need to calculate the slope of the line. The slope m is found by the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of the two points. Using this formula, the slope is (10 - (-8)) / (6 - 2) = 18 / 4 = 4.5.

Next, we can write the point-slope form of the equation using one of the points, for example (2, -8): y - (-8) = 4.5(x - 2). Simplifying this, we get y + 8 = 4.5x - 9. To convert to standard form, we rearrange the equation to have integer coefficients for x and y and set it to equal zero. The equation becomes: -4.5x + y + 17 = 0. Multiplying through by -2 gives us the standard form of the equation: 9x - 2y - 34 = 0.

Answer 2

y = 4.50x +-17

Step-by-step explanation:

Step 1: Calculating Slope (m).m = y2-y1x2-x1m = 10--86-2m = 184m = 4.50Now putting value of m in equation (i)y = 4.50x + b

Step 2: Calculating Y-intercept (b).Lets choose the first point, (2,-8) for calculating y-intercept:y = mx + b-8 = 4.50(2) + b-8 = 9 + b-17 = bb = -17