Question

Write the equation of the line that passes through the points left bracket, 4, comma, minus, 3, right bracket(4,−3) and left bracket, 8, comma, 5, right bracket(8,5). put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

To find the equation of the line that passes through two given points in point-slope form, we first calculate the slope using the formula (y2 - y1) / (x2 - x1). Substituting the coordinates of the points, we find the slope is 2. Next, we choose one of the points and use the point-slope formula, y - y1 = m(x - x1), to find the equation. Simplifying the equation, we obtain y = 2x - 11.

Step-by-step explanation:

To find the equation of the line that passes through the points (4, -3) and (8, 5), we can use the point-slope form of a linear equation. The formula for the point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

First, we need to find the slope of the line. The slope, m, can be calculated using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the points into the formula, we get m = (5 - (-3)) / (8 - 4) = 8 / 4 = 2.

Next, we choose one of the given points, let's say (4, -3), and substitute the values into the point-slope formula. Plugging in the values, we have y - (-3) = 2(x - 4). Simplifying the equation, we get y + 3 = 2x - 8. Finally, rearranging the equation to fully simplified point-slope form, we have y = 2x - 11.