Math Problem Statement

Without simplifying, identify the slope of the line given by the equation y - 5 = -2(x + 5). Then identify one point on the line.

Solution

The equation provided in the image is:

y5=2(x+5)y - 5 = -2(x + 5)

Step 1: Identify the slope

This is in point-slope form, which is:

yy1=m(xx1)y - y_1 = m(x - x_1)

Where:

  • mm is the slope of the line.
  • (x1,y1)(x_1, y_1) is a point on the line.

Here, we can see that m=2m = -2. Thus, the slope is -2.

Step 2: Identify a point on the line

Looking at the equation:

y5=2(x+5)y - 5 = -2(x + 5)

It is similar to yy1=m(xx1)y - y_1 = m(x - x_1), so comparing with the point-slope form, we see:

  • x1=5x_1 = -5
  • y1=5y_1 = 5

Thus, one point on the line is (-5, 5).

Summary:

  • Slope: -2
  • Point on the line: (-5, 5)

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. How do you convert an equation from point-slope form to slope-intercept form?
  2. How does the slope of a line affect its steepness?
  3. Can you find another point on the line by substituting a different value for xx?
  4. How would you graph the line using the slope and the point found?
  5. What is the y-intercept of this line?

Tip: The slope tells you how much the y-value changes for every unit increase in the x-value. If the slope is negative, the line will slope downward.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Point-Slope Form

Formulas

y - y1 = m(x - x1)

Theorems

Point-Slope Form Theorem

Suitable Grade Level

Grades 8-10