234k views
3 votes
Write an equation of the line passing through each of the following pairs of points.

(7, −3), (8, −7)

User Atyz
by
7.7k points

1 Answer

5 votes

Final answer:

The equation of the line passing through the points (7, -3) and (8, -7) is found by first calculating the slope (m = -4), then using the point-slope form with one of the points to establish y = -4x + 25 as the final equation in slope-intercept form.

Step-by-step explanation:

To write an equation of the line passing through the points (7, -3) and (8, -7), we first find the slope (m) of the line. The slope is obtained by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the points the line passes through. Substituting the given points into the formula, we get:

m = (-7 - (-3)) / (8 - 7) = -4 / 1 = -4

Now that we have the slope, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1). We can take either of the given points for (x1, y1). Using (7, -3), we substitute into the formula:

y - (-3) = -4(x - 7)

To find the y-intercept (b), we simplify the equation to the slope-intercept form, y = mx + b:

y + 3 = -4x + 28

y = -4x + 25

Thus, the equation of the line passing through the points (7, -3) and (8, -7) is y = -4x + 25.

User Adam Erickson
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories